.■ . , f*r^'i:tliiJ;' .. 'Hmj (ft 1 ... ...
(■■ &*'y& ■ . '. >:.^m *:•■■•■■  ■ ■
■ ■ ■ ■ v : ■ I ..:,:.. ........... .. .. . .
';■■ :M ■
"^mniihJiiAii/Aiiiifl^JlHil'fa'JirtTi ■ ■*
". i T[ — 5 "" ' "
II V.\:'L ■.:'■. ... ■ ..^ . . ' .__ . . ^ '
:':..■■ '■' **''■. ■.■.■■...■ • ■ ■
. ■ • ».... . .
fill >.■ ■
.^lUt^l   ill ilip ,
■ ■ " .•■,.,,■•■ . . ... ■....:
•■'■'. iti :gfc  •■■ "■ '
■
1
PRESTON POLYTECHNIC
LIBRARY & LEARNING RESOURCES SERVICE
This book must be returned on or before the date last stamped
5
sfrti
y
Evolution
of
Particle Physics
A volume dedicated
to
Edoardo Amaldi
in his sixtieth birthday
BRITISH LIBRARY
Edited by M. Conve^si LE
16 JAN 1978
I
Y 2 7469
ACADEMIC PRESS • new york and london
ACADEMIC PRESS INC.
Ill Fifth Avenue
New York 3, N, Y.
United Kingdom Edition
Published by
ACADEMIC PRESS INC. (London) Ltd.
Berkeley Square House, London W. 1
Copyright © 1070, ay Academic Press Inc.
ALL RIGHTS RESERVED
NO PART OF THIS BOOK MAY BE REPRODUCED IN ANY FORM,
BY PHOTOSTAT, MICROFILM, OR ANY OTHER MEANS,
WITHOUT WRITTEN PERMISSION FROM THE PUBLISHERS.
Library of Congress Catalog Card Number: 70 J 17640
ACCESSION No.
128830
CLASS No.
12 OCT 1978 J
H
PRINTED IN ITALY
To Edoardo Amaldi
in his sixtieth birthday
Biographical Note
Edoardo Amaldi was born in Carpeneto Piacentino, Piacenza, on Sep
tember 5, 1908. He graduated from the University of Rome in 1929. In the
years 193136 he consolidated his scientific formation at the University of
Lipsia under P. Deoye, the Cavendish Laboratory at Cambridge directed
by Lord Rutherford, Columbia University in New York, and the Carnegie
Institute in Washington. He has been professor of experimental physics at
the University of Rome since 1937.
After a forced absence due to the second world war, Amaldi is again
in Rome at the end of the Italian participation to the conflict. He was Director
of the former Center of Nuclear Physics of the Italian C.N.R, from 1945
to 1952, VicePresident of U1PPA from 1948 to 1954, Director of the Physics
Department of the University of Rome from 1949 to I960, Secretary General
of CERN from 1952 to 1954, Director of the Roman Section of INFN from
1952 to 1960, Director of the « Scuola di Pcrfezionamento in Fisica» in
Rome from 1952 to 1966, Vice Director of CERN in 1954 and 1955, Vice
President of the Italian CNRN, later CNEN, from 1956 to 1960, Pres
ident of UIPPA from 1957 to I960, Chairman and later Member of the
EURATOM Scientific and Technical Committc from 1958 to 1961, Chairman,
from 1958 to I960, and Member, from I960 to the end of 1969, of the CERN
Scientific Policy Committee, President of INFN and Member of the CNEN
Directive Committee from I960 to 1965, VicePresident of INFN from 1965
to 1968, Chairman of the European Committee for Future Accelerators
(ECFA) from 1963 to the beginning of 1970, when he became President of
the CERN Council.
Amaldi is a member of the «Accademia Nazionale dei Lincei », the
« Accademia Nazionale dei XL», the « Accademia Pcloritana», the « Acca
demia delle Scienze di Torino », the « Istituto Lombard© », the « Accademia
Nazionale di Scienze, Lettere ed Art! di Modena», the « Accademia Pu
gliese detle Scienze », the « Istituto Nazionale delle Profession!, delle Arti
e delle Scienze », the « Accademia Leopoldina», the Royal Society, the
Royal Society of Sciences of Uppsala, the Academy of Sciences of the USSR,
the Royal Institution of Great Britain, the American Philosophical Society
VI Biographical note
of Philadelphia, the National Academy of Sciences, the American Academy
of Arts and Sciences of Boston, the International Academy in Astronautics,
the « Academic Royalc Neerlandaise ».
Amaldi has received a number of prizes: one from the International
Columbus Association, also the « Premio IbbicoReggino », « Premio Righi »,
«Premio Sella », « Premio Uranio »... He is doctor honoris causa from the
University of Algiers. He has been awarded the Seal of the Sorbonne and,
recently, the golden medal of the Italian Physical Society,
Contents
Biographical Note , P a § v
Presentazione . , , , ,,.».. » K
Foreword , >J Xlt
Edoardo Amafdi et le CERN . . . . » *V
.d Edoardo Amaldi » XDE
7b Edoardo Amaldi, on his sixtieth birthday » xxi
Scientific Contributions » xxm
L. W. Alvarez  Recent developments in particle physics ...» 1
N. Cabibbo and L. Maiani  Weak interactions and the breaking
of hadron symmetries » 50
G. Cocconi  The role of complexity in nature » 81
B. Ferretti  Channeling of ullrarelativislic charged particles in
crystals » 88
G. Fidecaro and M. Fidecaro  Experimental work on coherent
scattering of highenergy hadrons by light nuclei » 95
C. Fkan/lnliii and G, Stoppini  The determination of the axial
vector coupling for strangeness nonchanging currents .... » 114
S. Fubini  Old problems and new ideas in elementary particle
physics ■ }> '''
R, Gatto  High energy e"e~ annihilation into hadrons .... » 138
G. Giacomelli  New frontiers of highenergy physics » 148
M. Goldhaber and G N. Yang  The K°K> system in pp anni
hilation at rest ............■■ » l71
T. D. Lee  Symmetry principles in physics .......... » 176
A. W. M urrison  The design and use of large electron synchrotrons » 1 84
VIH Contents
L. Michel and L. A, Radicati  Breaking of the SU 3 x$U 3 sym
metry in hadronic physics , pag. 191
A. Paoletti and S. Sciuti  Structure of matter investigations by
thermal neutrons in Rome » 204
B. Pcxntecorvo  Search for new stable particles ....... » 210
R. A. Rtcci  The isobaric analog resonances in phenomeno logical
nuclear spectroscopy » 21S
B. Rossi  The Crab nebula. Ancient history and recent discoveries » 237
C. Rubbia  The K L — K s mass diiTercnce » 257
J. Steinberger  Suggestion for a more precise measurement of
the %_ phase » 268
V. F. Weisskopf  An amateur's view of particle physics .... » 273
G. Wick  Some questions concerning adiabatic transformations » 287
R. R. Wilson  Range and straggling of muons » 294
A. Zichichi  The Basic SU a mixing: ^±7% ........ » 299
List of Papers by Edoardo Amaldi » 335
Presentazione
Circa un anno fa, il 5 settembre del 1968, Edoardo Amaldi ha varcato il
limite simbolico della matura eta. Eravamo con lui, in quelVoccasione, in un
piccolo gruppo di amid seduti intorno al tavolo di un modesto ristorante Vien
nese, durante una breve pausa della International Conference on High Energy
Physics. Non vifu alcun festeggiamento. Ma al termine della colazione un breve
scambio di battute tra alcuni di noi segno la ripresa di una iniziativa che era
stata interrotta da motivi di carattere contingente. Quell 'iniziativa si conclude
ora con la pubblicazione del presente volume, il quale — tardivamente ma non
meno affettuosamente—vuole appunto commemorare il 60° compleanno di
Edoardo Amaldi.
II titolo Evolution of Particle Physics sembra appropriato ai quaranta anni
di vita da fisico vissuti dalVuomo cui il libro e dedicato. La vita scientifica di
Edoardo Amaldi si svolge infatti su un arco di secolo che ha visto nascere ed
evolversi fino aWattuale livello di complessita Vintero campo della fisica delle
particelle. Prima degli anni 30 si conoscevano solo due particelle, ritenute i
costituenti fondamentali di tutto VUniverso. A parte la scoperta di nuove e
nuove particelle {che non fa piii senso chiamare oggi « elementari ») il concetto
di costituente fondamentale si e trasferito in quelVarco di secolo dal mondo
del nucleo atomico a quello degli stessi corpuscoli di cui esso e formato, attra
verso modelli ed ipotesi come quella — la piu recente — associata al nome dei
« quarks ». QuelVarco di secolo ha visto mutare per molti ordini di grandezza
— dai milioni ai miliardi di elettronvolt — le energie tipiche dei fenomeni inve
stigati edha vissutofin dalla nascita tutte lefasi dello sviluppo degli acceleratori:
dalla prima macchina elettrostatica operante nella regione dei cento keV, fino
ai giganteschi acceleratori per protoni da centinaia di GeV, ora in costruzione
o in progetto. Uevoluzione di quel quaranfanni coinvolge la fisica teorica cosi
come le tecniche sperimentali. Sorge e si sviluppa il nuovo campo delle intera
zioni deboli, Videa del mesone come agente delle forze nucleari, la nuova elettro
dinamica quantistica, la teoria dei campi nella sua versione moderna; mentre
dalla camera a nebbia e dai contatori proporzionali usati con una elettronica
primitiva, si passa alle gigantesche camere a bolle di oggi ed ai complessi sistemi
elettronici e di camere a traccia impulsate elettricamente, caratteristici degli
odierni esperimenti presso i grandi acceleratori di particelle.
X Presentazione
Alia scena di questa evoluzione — cut il nostro paese e VEuropa hanno dato
ben tangibili contributi — Edoardo Amaldi ha partecipato come « at tore »
sempre presente. Vi ha partecipato sia come scienziato avente al suo attivo una
vastissima gamma di ricerche, sia assumendo a livello nazionale ed europeo
pesanti e numerose responsabilitd direttive. Perche prima ancora che un grande
organizzatore egli e stato ed e un uomo di scienza: un fisico. Nel suo primo
lavoro sperimentale, compiuto da studente non ancora ventenne, e Vinizio di
un'attivitd di ricerca, sempre viva e di frontiera, che si protrarra ininterrotta
mente per i successivi quaranfanni, nonostante i pesanti impegni connessi alle
cariche direttive sopra accennate.
Nei primi anni la ricerca si svolge in seno aWormai famoso gruppo dei
« ragazzi di Corbino » dei quali Edoardo e allora il piii giovane. II gruppo,
formato da giovani di primissimo ordine e dominato daW eccezionale personalita
scientifica di Enrico Fermi, e destinato a disfarsi nel giro di un decennio, sotto
Vincalzare degli eventi che preludono alio scoppio della seconda guerra mondiale.
Ma in questi died anni si compiono lavori destinati a restare nella storia della
fisica. Amaldi partecipa attivamente alle ricerche sperimentali, le quali spa
ziano dalla fisica atomica, alia spettroscopia molecolare, fino ai classici esperi
menti sulV interazione dei neutroni con la materia. Tra i risultati piii salienti
di questi esperimenti sono la radioattivitd indotta dai neutroni, con la produ
zione di numerosi nuovi radioisotopi, la scoperta del rallentamento neutronico,
la determinazione delle piii importanti proprietd dei neutroni lenti con la prima
verifica sperimentale del teorema ottico, la prova diretta della diffrazione dei
neutroni veloci da parte dei nuclei.
Ogni possibilitd di ricerca e virtualmente bloccata negli anni tragici della
guerra. Gid prima, con la scomparsa prematura di Ettore Majorana e poi con
Vesodo di quasi tutti i componenti della Scuola di Roma, questa minaccia di
estinguersi. E Amaldi a salvarla, con la sua presenza costante, particolarmente
nei momenti dijficili, con la sua dedizione assoluta, con il suo esempio, con la
volontd di riprendere Vattivita di ricerca non appena Voccasione se ne presenta.
E la sua attivita scientifica negli anni del dopoguerra si orienta verso lo studio
dei raggi cosmici prima, poi delle particelle elementari. Con tecniche elettro
niche che preludono alia futura complessitd degli apparati usati presso gli acce
leratori di alta energia, investiga le proprietd dei mesoni cosmici a grandi pro
fondita. Con la tecnica delle emulsioni nucleari esposte ad alta quota mediante
palloni sonda, studia il comportamento dei pioni carichi, dei mesoni K e degli
iperoni presenti nella radiazione cosmica ed osserva un probabilissimo esemplare
di stella da annichilazione antiprotonenucleone precedendo la scoperta conclusi
va delV antiprotone compiuta a Berkeley nel 1955. Poi dal 1955 al 1959 guida il
gruppo di Roma che insieme ad un gruppo di Berkeley compie le prime ricerche
sistematiche suW annichilazione degli antiprotoni prodotti con il Bevatron.
Presentazione XI
Negli anni successivi troviamo Amaldi — ormai piii che cinquantenne —
ancora in prima fila, coinvolto in arditi esperimenti presso i grandi accelerator!
diparticelle: dalla ricerca dei monopoli di Dirac, alio studio della polarizzazione
dei protoni di rinculo nelVurto elettroneprotone, fino alle recentissime espe
rienze di elettroproduzione.
II contributo di Amaldi come organizzatore della fisica in Italia e in Europa
e stato poi veramente eccezionale. Questo volume inizia con uno scritto di
Francis Perrin che illustra il contributo particolare apportato da Amaldi alia
costituzione e agli sviluppi del CERN. Con analogo entusiasmo e con la stessa
dedizione, egli disimpegnava in queWepoca le altre pesanti cariche direttive in
seno alVUniversita di Roma, alVINFN, al CNEN, ecc. : mai trascurando
V attivita didattica; mai tralasciando di seguire da vicino le esperienze in cui
era coinvolto, ne gli sviluppi delle ricerche anche in settori lontani da quello del
suo immediato interesse; promuovendo anzi la costituzione di nuovi gruppi di
ricerca a Roma nei campi delle basse temperature e della fisica spaziale; mai
rifiutandosi di sacrificare la sua attivita personate a favore di iniziative — come
ad esempio il « Pugwash » — che dalV autorita scientifica della sua persona
potessero trarre vantaggi per le generazioni a venire. E questa capacita di disim
pegnare con continuita, ininterrottamente sopra un arco di decenni, una cost
varia e complessa attivita, appare quasi prodigiosa alia luce dello stile sobrio,
semplice, disinvolto, sempre limpido e sereno, tipico di Amaldi. Lo ricordo
ancora negli anni piii oscuri deW occupazione nazista — quando piii o meno
nascosti nel seminterrato di un liceo romano conducevamo lontani dalVUni
versita bombardata i nostri esperimenti sui mesoni cosmici — incontrarsi spesso
con noi, sempre esattamente aWora prefissata per V appuntamento, come se
intorno tutto fosse normale; e sempre recando, insieme al contributo della sua
cultura e della sua sensibilita difisico, il sostegno — in quel giorni ancora piii
prezioso — di una fondamentale fiducia nelVavvenire.
Nel quarto di secolo trascorso da quel ricordo, passato il traguardo dei
sessanf anni, ritroviamo in lui quella stessa fondamentale fiducia. Essa gli ha
permesso di superare in tutta serenitd le gravi crisi che in quel periodo hanno
travagliato la ricerca scientifica e la scuola italiana; e poiche e parte integrante
della sua stessa personalitd, essa gli sard sempre accanto nei lunghi anni a venire.
Noi suoi amici — anche i tanti che non hanno potuto manifestargli la low stima
e la loro simpatia con uno scritto su questo libro — esprimiamo il fervido augurio
che la scuola italiana, la ricerca scientifica europa e la fisica nel suo complesso,
continuino per molti e molti anni a ricevere, come sempre in passato, i frutti
della sua instancabile operositd e della sua equilibrata saggezza.
Marcello Conversi
Roma, Ottobre 1969
Foreword
About one year ago, the 5th of September, 1968, Edoardo Amaldi cele
brated his sixtieth birthday. On that occasion we were with him, a small group
of friends, sitting in a modest restaurant in old Vienna, during a break in the
1968 Rochester International Conference on High Energy Physics. There
was no ceremony. But after lunch, a few words exchanged between some of us
marked the resumption of an enterprise interrupted by the exigencies of our
professional lives. That enterprise is now concluded with the publication of
the present volume, which tardily, but no less affectionately, commemorates
Amaldi' s sixtieth birthday.
The title Evolution of Particle Physics seems very appropriate to the man
to whom the book is dedicated, with his scientific life covering the entire period
from the birth of the field of particle physics to its development to the present
level of complexity. Before 1930 only two particles were known and believed
to be the fundamental bricks of the whole universe. Since then, not only have
many new particles been discovered — which can no longer logically be called
« elementary » — but even the idea of a few fundamental bricks has moved
from the realm of the atomic nucleus to that of its own consistuents through
hypotheses and models such as that of the « quarks » {the most recent one).
The energies involved in the phenomena investigated have changed from the
million to the billion electronvolt region; while the first particle accelerator,
an electrostatic machine operating at some tenths of a mega electronvolt,
evolved to the giant machines now under construction or in project, for protons
of several hundred giga electronvolts. The evolution of the last forty years
involves theoretical physics as well as experimental techniques. The new field
of weak interactions, the idea of the meson as the agent of nuclear forces, the
new quantum electrodynamics, the modern version of field theory, all evolved
in these forty years; whereas from the cloud chamber and the proportional
counter used with a primitive electronics, one has ended with the huge bubble
chambers and the gigantic electrically pulsed track detectors, associated with
complex electronics, now currently used in highenergy physics.
Amaldi was always present as an « actor » on the stage of this evolution,
to which our country and Europe have given an appreciable contribution. He
Foreword XJII
has been there both as a scientist with a vast spectrum of interests and as an
organizer of Italian and European scientific research. Notwithstanding that he
is a great organizer, he is first and foremost a physicist.
His first work, carried out when he was a nineteenyearold student, was
the beginning of a scientific career always on the frontier of physics, lasting
uninterruptedly for over forty years. At the beginning, his research was car
ried out in the now famous group of the « Corbino's boys », where Edoardo
was the youngest. The group, dominated by the scientific personality of Enrico
Fermi, included a number of first class young scientists. Hounded by the events
preceding the outbreak of the second world war, the group was destined to
disperse in about a decade. But in these ten years work was accomplished which
remains in the history of physics. Amaldi actively participated in all the experi
mental research, which ranged from atomic physics to molecular spectroscopy,
up to the classic experiments on the interaction of neutrons with matter. Among
the most significant results are the radioactivity induced by neutrons, the pro
duction of new radioisotopes, the discovery of the slowing of neutrons, the first
experimental check of the optical theorem, the direct proof of the diffraction
of fast neutrons by nuclei.
Any possibility of research was virtually eliminated in the tragic years of
the war. Even before, after the premature disappearence of Ettore Majorana
and the exodus of almost all components of the Roman school, the latter was
near extinction. Amaldi saved it by his continuous presence, especially in difficult
moments, by his total dedication, his example, his will to recommence scientific
activity as soon as circumstances would allow. In the postwar years his interest
moved first to the field of cosmic rays and later to elementary particle physics.
He investigated the properties of cosmic ray muons underground, using an
electronic technique which prefigured the future complexity of the apparatuses
later employed with highenergy accelerators. Then he studied the behaviour
of cosmic ray pions, Kmesons, and hyperons, using nuclear emulsions exposed
in balloon fligths, and observed a very probable example of an antiproton
nucleon annihilation star, just before the conclusive discovery of the antiproton
at Berkeley in 1955. Subsequently, from 1955 to 1959, he led the Roman group
which together with a group at Berkeley performed the first systematic inves
tigation of the annihilation of the antiprotons produced by the Bevatron.
In the following years we find Amaldi — now more than fifty years old — still
in the first line, involved in bold experiments carried out with large particle
accelerators. They include a search for Dirac monopoles, a study of the polar
ization of recoil protons in electronproton collisions, and the very recent experi
ments on pion electroproduction.
The contribution of Amaldi to the organization and development of physics
in Italy and Europe has been really outstanding. This book, starts with a paper
XIV Foreword
by Francis Perrin which illustrates particularly AmaldVs contribution to the
creation and development of CERN. With the same enthusiasm and dedication,
he performed in that period the heavy duties associated with the directive respon
sibilities he had at the University of Rome, the Italian Institute of Nuclear
Physics (INFN), the National Committee for Nuclear Research (CNRN,
later CNEN), etc.; never neglecting his educational duties, never failing to follow
closely the experiments in which he was personally involved, nor the develop
ments of research also in fields far from his immediate interest, promoting,
in fact, the creation of new groups in Rome operating in low temperature and
space physics, never refusing to sacrifice his personal activity in favour of ini
tiatives — such as, for example, « Pugwash » — which through the weight of his
scientific authority could bring advantages to the generations to come.
The capacity to engage in activities so various and complex, continuously
and uniterruptedly over a period of decades, appears almost prodigious in the
light of AmaldVs personality, sober, informal, easy going, always clear minded
and serene. I still remember him in the darkest years of the Nazi occupation
(when more or less hidden in a Roman lyceum, we carried out far from the
bombarded University our experiments on the cosmic muons) meeting often
with us, always exactly at the prefixed time, as if everything around were
normal. And always bringing, together with his culture and physical good sense,
the support — even more precious in those days — of a fundamental confidence
in the future.
A quarter of a century later, we still find in him the same fundamental
confidence. It has allowed him to overcome the severe crisis that scientific
research and the Italian school suffered in that period. And since this confi
dence is an integral part of his personality, it will always accompany him in
the long years to come. His friends — including the many friends who were
unable to exhibit their esteem and affection with a contribution to this book —
express with me the warmest wish that the Italian school, European scientific
research and physics at large, will continue for many and many years to come
to profit, as in the past, from the fruits of his tireless work and serene wisdom.
Marcello Conversi
Rome, October 1969
Edoardo Amaldi et le CERN
Depuis une trentaine d'annees les progres les plus significatifs de la phy
sique fondamentale se sont produits dans le domaine des particules ephe
meres creees par des collisions entre nucleons a des energies de plus en plus
elevees. Tant que les rayons cosmique on ete la seule source de particules
de haute energie pouvant donner lieu a de telles collisions, les physiciens
europeens travaillant en Europe, avec les techniques des emulsions nucleaires
ou des chambres a brouillard, ont eu une grande part dans les decouvertes
de particules nouvelles qui ont fait pressentir la richesse imprevue et l'etran
gete de ce domaine ou un nouveau bouleversement des fondaments de la
Science commencait a s'esquisser.
Mais, des la mise en service des accelerateurs americains de quelques
gigaelectronvolts, le Cosmotron de Brookhaven puis le Bevatron de Ber
keley, il est clairement apparu aux physiciens les plus avertis que si de grands
accelerateurs n'etaient pas construits en Europe, les scientifiques europeens
ne pourraient plus participer effectivement au progres de cette partie de la
Science, celle ou des lois vraiment nouvelles pouvaient etre decouvertes,
sans emigrer vers l'Amerique, ce qui ferait peu a peu perdre a la grande
majorite des nouvelles generations d'etudiants euroeens tout contact vivant
avec la Science en formation.
Edoardo Amaldi fut un des quelques hommes qui eurent tres tot et tres
vivement conscience de ce danger, et qui, comprenant que la construction
d'un accelerateur equivalent aux futurs accelerateurs americains exigerait des
moyens financiers et humains beaucoup plus grands que ceux qu'aucun Etat
europeen, agissant isolement, pourrait ou voudrait consacrer a une telle rea
lisation, entreprirent une action visant a associer la plupart des pays d'Europe
en vue de la construction en commun d'un accelerateur des tres haute energie.
Cette action, trouvant heuresement un climat politique favorable, devait
aboutir relativement rapidement a la signature en 1953, par une douzaine
d'Etats europeens, d'une convention creant un Centre Europeen de Recherche
Nucleaire, le CERN, etabli a Geneve par un choix unanime, qui avait
comme object principal la construction et 1' exploitation scientifique d'un grand
accelerateur. Le remarquable succes de cette entreprise, tant pendant la
phase de la construction que pendant celle de 1' exploitation, succes qui a
XVI Edoardo Amaldi et le CERN
permis a l'Europe de reprendre, apres une dizaine d'annees d'eclipse, une
place de premier rang en physique des hautes energies, est certainement du
au fait qu'elle a ete concue puis animee par des hommes de science qu ne
perdaient jamais de vue le but poursuivi et qui faisaient aisement abstraction
de toute rivalite nationale mesquine.
Les deux physiciens qui ont par leur action le plus contribue a la creation
du CERN sont certainement Pierre Auger et Edoardo Amaldi. C'est a la
suite d'entretiens qu'il eut avec l'un et l'autre, que Rabi chef de la delegation
americaine a l'Assemblee generate de l'UNESCO qui se tint a Florence au
printemps de 1950, fit adopter une resolution chargeant cette organisation
mondiale de susciter la creation d'un laboratoire europeen de physique des
hautes energies. Pierre Auger alors Directeur du Departement des Sciences
exactes et naturelles de l'UNESCO, prit en main la mise en oeuvre de cette
resolution en faisant etablir un projet precis, qui puisse etre propose aux
gouvernements, par un groupe d'experts, physiciens des principaux pays
interesses choisis en accord avec Amaldi. Des la premieere seance de ce
groupe d'expert, Auger en confia la presidence a Amaldi, reconnu par tous
comme le plus qualifie, pour en animer les travaux.
Quand en mai 1952 une Organisation provisoire du futur CERN fut
decidee par un accord entre les gouvernements, Amaldi en fut nomme Secre
taire General. A ce poste, qu'il conserva jusqu'en octobre 1954, il dirigea la
preparation de la convention definitive, avec ses annexes fmancieres, et les
reglements qui donnerent au CERN sa grande efficacite de fonctionnement.
Durant cette periode de tres important contrats furent prepares et signes
avec l'architecte et les principales compagnies qui devaient construire ou
fabriquer les batiments et les premiers gros constituants (dont l'aimant) du
premier accelerateur, le synchrocyclotron de 600 MeV, dont devait etre
dote le CERN. De nombreux contrats relatifs a la construction du synchro
tron a protons de 25 GeV, appareil principal du futur laboratoire, furent
egalement prepares sous la direction d'Amaldi.
Apres la nomination, en octobre 1954, de Felix Bloch comme premier
Directeur General du CERN, Amaldi accepta encore de consacrer la plus
grande partie de son activite au CERN pendant 6 mois en qualite de Directeur
General adjoint. Pendant les annees cruciales de formation et d'orientation
du CERN, durant lesquelles s'est forme l'esprit qui devait l'animer quand la
recherche scientifique a pu y commencer, c'est Amaldi qui a joue avec con
tinuity le role principal, en montrant un grand sens de Taction politique, mais
en pensat et en agissant toujours en grand physicien, qui ne perdait jamais
de vue l'objectif scientifique de cette vaste entreprise commune europeenne.
Malgre tant de temps et d'effort donnes a des activites administrative,
Amaldi a su rester un vrai scientifique et aussitot qu'il l'a pu il s'est de nouveau
consacre a ses activites universitaires a Rome, enseignement et direction d'un
Institut de Recherche tres vivant. Et, ce qui est particulierement remarquable,
Edoardo Amaldi et le CERN XVII
il a su reprende luimeme une activite originale de recherche. C'est ainsi
qu'il a effectivement participe, au cours d'un sejour a Berkeley, a la tres
belle experience qui apporta, en octobre 1956, la preuve definitive de l'exi
stence des antiprotons par l'observation et l'analyse precise d'etoiles produites
par leur annihilation dans des emulsions nucleaires.
C'est ce qui permet de comprende pourquoi, quand au debut de 1963
il apparu necessaire d'envisager pour l'Europe, en face de project americains
activement pousses, une deuxieeme etape de collaboration en physique des
hautes energies, c'est encore Amaldi que le Comite des Directives Scientifi
ques du CERN designa a l'unanimite pour presider un Comite europeen
sur les futurs Accelerateurs, l'ECFA, pourtant deliberement forme par des
physiciens en pleine activite de recherche et nettement plus jeunes que ceux
avaient prepare la fondation du premier CERN. Le rapport presente par
Amaldi des le mois de juin 1963 recommandait la construction, en comple
ment du PS de 28 GeV, d'anneaux de stockgae a intersections (les ISR)
devant permettre une exploration a tres faible intensite vers les tres hautes
energies, et la creation d'un nouveau laboratoire ayant comme equipement
principal un synchrotron a protons de 300 GeV (environ dix fois plus grand
que celui du premier laboratoire europeen). La construction des ISR fut
decidee par le Conseil du CERN en juin 1965 et doit s'achever en 1971, mais
malgre un rapport technique detaille presente en 1964 par l'ECFA, aucune
decision ne fut prise relativement a l'accelerateur de 300 GeV. Afin de refaire
un examen approfondi des besoins europeens et des possibilites techniques
de realisation dans le domaine des tres hautes energies, l'ECFA fur renouvele
en mars 1966, groupant alors une soixantaine de physiciens, toujours sous la
presidence d'Amaldi, qui presenta au Conseil du CERN en juin 1967 un
nouveau rapport confirmant la recommandation de la realisation du synchro
tron de 300 GeV propose en 1964 et tracant les grandes lignes du programme
de son utilisation scientifique. C'est a la suite de ce rapport que furent adres
sees au President du Conseil du CERN les premieres lettres officielles de
gouvernements declarant leur intention de participer a un deuxieme labora
toire europeen dote d'un accelerateur de 300 GeV, si un nombre suffisant
de partenaires pouvaient etre rassembles.
La grande valeur des considerations generates justifiant les propositions
presentees par Amaldi en tant que president de l'ECFA doit etre soulignee.
Dans ses rapports au Comite des Directives Scientifiques ou au Conseil du
CERN, on sent qu'il ne s'est jamais laisse influencer par des arguments de
prestige ou de rivalite avec l'Amerique ou l'URSS, ni par le desir d'etablir
des records ou l'attrait du gigantisme; ses raisons etaient toujours solidement
fondees sur l'interet scientifique et une utilisation optimum, a ce point de
vue, des grands moyens financiers inevitablement necessaires. C'est ainsi
qu'il a clairement montre que le choix d'une energie de 300 GeV pour le
2*
XVIII Edoardo Amaldi et le CERN
projet de futur accelerateur europeen, tandis que les Americains envisageaient
alors pour leur projet une energie de 200 GeV, ne resultait pas du desir d'at
teindre une energie un peu plus grande, avec peutetre, sans raison serieuse,
l'espoir de depasser le seuil d'apparition d'un phenomene nouveau, mais
que ce choix etait justifie par la prevision que Ton obtiendrait, dans le domaine
d'energie autour de 10 GeV, des faisceaux secondaires de particules etranges
(mesons K ou hyperons) et de neutrinos d'un ordre de grandeur plus intense
avec un faisceau primaire de protons de 300 GeV au lieu de 200 GeV, et que
c'etait le tres grand accroissement d'intensite de ces faisceaux secondaires
d'energie relatievement basse qui permettait le plus d'esperer des progres
decisifs dans la decouverte et la comprehension des lois fondamentales regis
sant le monde des particules elementaires.
Ce sont d'ailleurs principalement ces raison s qui ont conduit les Ame
ricains a modifier leur projet initial en entreprenant la construction d'un
accelerateur devant bien avoir initialement l'energie prevue de 200 GeV,
mais pouvant etre, quelques annees apres, transforme, sans depense excessive,
de facon a atteindre 400 GeV. Similairement, quand en juin 1968 le gouver
nement britannique fit savoir qu'il ne pourrait pas, pour des raisons finan
ciers, s'associer a la realisation du deuxieme laboratoire du CERN, malgre
l'excellence du projet presente, et qu'il fallut pour sauver cette entreprise
essentielle pour l'Europe, envisager un projet moins onereux, Amaldi, parlant
toujours en tant que president de l'ECFA mais avec sa puissance person
nels de persuasion, reussit a convaincre tous les membre du Comite des
Directives Scientifiques, que meme au prix d'autres sacrifices il fallait abso
lument garder la possibilite d'atteindre finalement l'energie de 300 GeV
meme s'il apparaissait inevitable de proposer aux gouvernements une pre
miere etape ne depassant pas l'energie de 200 GeV. II ne pouvait accepter
que des contingences sans doute passageres risquent de compromettre defi
nitivement ce qu'il voyait clairement etre la caracteristique la plus promet
teuse a longue echeance du futur accelerateur europeen.
Ainsi, Edoardo Amaldi a ete depuis une vingtaine d'annees un des grands
promoteurs du developpement de la physique des hautes energies en Europe,
au premier rang de ceux qui estiment que la participation active a ce domaine
de la recherche scientifique fondamentale est un facteur important pour
conserver une ame a notre civilisation moderne menacee d'etouffement spi
rituel par l'aspect materiel du progres technique. II ne s'est jamais derobe
quand on lui a demande de sacrifier ses activites personnelles de physicien
car il avait conscience de pouvoir aider a preparer, pour toute une generation
de jeunes chercheurs de nos vieux pays d'Europe, la possibilite de contribuer
a certains des progres les plus significatifs de la Science.
Francis Perrin
A Edoardo Amaldi
Piuttosto che strizzarmi il cervello per scrivere una pagina di fisica piu
o meno interessante preferisco offrire a questo libro e a te personalmente
una pagina di ricordi di un'amicizia di oltre quaranta anni.
II prologo si stende su due o tre generazioni, originanti da Bozzolo.
Mio padre raccontava che da bambino, ormai circa un secolo fa, gli dice
vano per farlo star buono che se era cattivo lo avrebbero detto al Giudice
Amaldi, tuo Nonno. I nostri zii furono compagni al Collegio Ghislieri a Pavia
e ancor prima di conoscerti ho incontrato i tuoi zii e cugine e ascoltato un
corso sulla teoria delle funzioni di variabile complessa dato da tuo Padre.
Era cosi bello che malgrado non fosse obbligatorio e fosse a un'ora scomo
dissima non ne persi una lezione.
Noi ci siamo conosciuti verso il 1925 e andammo subito ad arrampicare
montagne insieme. Non dubito avrai ormai digerito, ma non dimenticato,
una scatoletta di antipasto sul Corno Piccolo. Allora — anche adesso — eri
roseo, atletico e bellino. Quando diventammo compagni per qualche corso
universitario ricorderai l'incarico di fiducia che avevi alle lezioni di Volterra,
oltre a quello di prendere gli ottimi appunti su cui imparammo vuoi il doppio
delta due che le distorsioni. Ci si preparava poi agli esami nella casa deimiei
genitori a Tivoli; una cosa semplice rispetto a quello che mi dicono richiedi
oggi ai tuoi studenti.
Lo studio con Fermi dal 1927 in poi e per tutti quelli che hanno avuta la
fortuna di parteciparvi un'esperienza indimenticabile, e se non bastasse
aveva come soggetto principale l'allora nuova meccanica quantistica. Fu que
sto certo il punto saliente della nostra formazione culturale come fisici.
Allora, a Via Panisperna, avemmo anche le visite dei nostri amici stranieri,
soprattutto l'indimenticabile Placzek e ogni tanto Majorana che ci strabiliava
coi suoi gruppi. Ricorremmo a tuo Padre perche la mia esperienza di alunno
mi aveva persuaso che se c'era una speranza di imparare la teoria dei gruppi,
era quella di farsela insegnare da lui. In risposta alle nostre richieste piut
tosto utilitarie, da fisici, egli ci disse che veramente si sarebbero dovuti studiare
anche i gruppi di Lie. Era profeta e si rallegrerebbe oggi a vedere VSU 3 e i
fisici curvi a studiarli.
XX A Edoardo Amaldi
Del lavoro a Roma voglio solo ricordare le docce di mercurio che pren
demmo al tempo degli atomi gonfi e la lampada per l'ultravioletto nello stesso
periodo, nonche la tua preziosa lastra Raman dell'ammoniaca ; pero non
tutti gli esperimenti avevano avventure cosi drammatiche, per fortuna.
II lavoro sui neutroni con Fermi e ormai parte della storia maggiore della
fisica. Dette occasione alia nostra breve permanenza a Cambridge, quando
stava per nascere Ugo jr., e alia nostra conoscenza con Rutherford. Piu tardi,
quando io ero ormai a Palermo, passammo Testate assieme in Dolomiti,
con i figlioli piccini, in cesti, sui prati d'Alba di Canazei.
Vennero poi gli anni tragici della guerra e delle persecuzioni. Eri a casa
mia in California quando scoppio la seconda guerra mondiale e mi ricordo
ancora le ansie di quel fatale settembre del 1939 e il tuo ritorno in Italia.
Rotte le comunicazioni per la durata della guerra, le prime notizie che
riebbi dall'Italia mi arrivarono a Los Alamos dove mi fu comunicato che i
militari Americani ti avevano rintracciato, secondo ordini ricevuti, appena
entrati a Roma.
Ci rivedemmo nel 1947 quando tornai per la prima volta a Roma e i
ricordi freschi della guerra erano il soggetto principale di conversazione.
Appresi cosi le tue peripezie in Libia e poi la tua fabbrica di timbri e altre
amenita del genere.
Piu tardi, quando si cominciava a parlare del CERN per cui avevi tanto
entusiasmo, se ne discusse a lungo, un'altra volta sotto i vecchi olivi diTivoli.
Seguirono le tue nuove visite a Berkeley intercalate dalle mie a Roma. L'ul
tima volta che sei venuto a Berkeley fu al tempo del lavoro sull'antiprotone
che ci ha dato occasione di scrivere di nuovo un lavoro insieme.
A un tempo dove le amicizie costanti e di lunga durata diventano sempre
piu rare e preziose auguriamoci che la nostra possa prosperare a lungo.
Emilio Segre
To Edoardo Amaldi, on His Sixtieth Birthday
Rather than contributing a more or less interesting page of physics, I
prefer to offer to this book a few personal recollections of a friendship which
has lasted for over forty years.
Its antecedents extend for two or three generations, originating in the
small town of Bozzolo, near Mantua. My father used to tell me of his child
hood, about a century ago. I thus learned that when he had done some
childish mischief, his parents told him that they would report it to Judge
Amaldi, Edoardo's grandfather; this threat was supposed to make him more
careful in the future. Our uncles were schoolmates in the distinguished
Collegio Ghislieri at the University of Pavia; and even before meeting you,
I knew your uncles and cousins. Furthermore, as an engineering student,
I had enrolled in a course on the theory of a complex variable which your
father gave at the University of Rome. It was such a fascinating course that
I did not miss a lecture although it was not a required course and was given
at an inconvenient time.
We met in 1926 or shortly after and we went mountain climbing together.
I am confident you will have by now digested but not forgotten the can of
antipasti on the Corno Piccolo, in the Gran Sasso d'ltalia group. At that
time — even as now — you were rosy complexioned and athletic. When we
took some University courses together, you were entrusted, as you may
remember, not only with the task of taking the superb notes with which we
prepared for the examinations, but also with another delicate task; and it
was your faithful help which allowed me to hear from Volterra himself the
double delta squared and the theory of distortions. At that time we prepared
for the examination at my parents' house in Tivoli. It was a simple job com
pared to what, I am told, you require from your present students.
Study under Fermi from 1927 on was an unforgettable experience for
all those who has the good luck of participating in it. For us it even has
the added poignancy of covering quantum mechanics in its early formative
phase. Without doubt this was the highlight of our cultural formation as
physicists. In those halcyon years in Via Panisperna we also had visits from
our foreign friends — first of all the unforgettable Placzek — from whom we
XXII To Edoardo Amaldi, on his sixtieth birthday
learned much and not only in physics, and furthermore Majorana, who once
in a while stunned us with his groups. We turned to your father for help,
because my experience as a student had convinced me that if there were any
hope of mastering group theory, it was through his teaching. Contrary to
our rather utilitarian approach, typical of young experimental physicists,
he told us that we should really study also Lie groups. He was a prophet,
and would rejoice seeing physicists using SU Z and beginning to appreciate
what was one of his chief interests.
Of our early experimental work in Rome I want to remind you only of
the « swollen atoms », of the mercury shower we took and of our hydrogen
arc for the ultraviolet and its explosion. Your precious ammonia Raman
spectrum is of the same period. However, luckily not all experiments had
such dramatic adventures.
The neutron work with Fermi is by now historical. It gave us also an
opportunity to spend some weeks at Cambridge and to meet Rutherford
just when Ugo Jr. was about to be born. A little later, when I was already
in Palermo, we spent a summer together at Alba di Canazei in the Dolomites,
carrying our little children in baskets on the alpine meadows.
Later we went through the tragic years of war and persecution. You
were at my house in Berkeley when the war broke out, and I vividly remember
the anxious days of the fatal September 1939 and you decision to return
to Italy.
Communications were interrupted for the duration of the war. The first
news from Italy reached me in Los Alamos in 1944, where I was told that
an American mission had been instructed to look for you on entering Rome.
We saw each other again in 1947, the first time I returned to Rome after
the war. War scars were visible everywhere, and the conversation centered
on war events. I thus learned of your adventures in Africa, of your small
rubber stamp factory to produce « unofficial » documents under the German
occupation of Rome, and of sadder events.
Later on, when the CERN project was in its formative stages, we discussed
it in detail once more under the olive trees of Tivoli. Your enthusiasm for
it, your arguments for the soundness of its approach to the problem of « big
physics » and for its possible wider beneficial implications, carried conviction.
Your visits to Berkeley interspersed with mine to Rome, followed. I think
it is now your turn to come to Berkeley again. The last time you visited me
at leisure was during the antiproton work, which gave us once more the
occasion to write a paper together.
At a time when long and constant friendships are becoming rare and
precious, let us hope that ours may thrive yet for a long time.
Emilio Segre
SCIENTIFIC CONTRIBUTIONS
Recent Developments in Particle Physics (*).
L. W. Alvarez
The Lawrence Radiation Laboratory  Berkeley, Cat.
When I received my B. S. degree in 1932, only two of the fundamental
particles of physics were known. Every bit of matter in the universe was
thought to consist solely of protons and electrons. But in that same year, the
number of particles was suddenly doubled. In two beautiful experiments,
Chadwick [1] showed that the neutron existed, and Anderson [2] photogra
phed the first unmistakable positron track. In the years since 1932, the list
of known particles has increased rapidly, but not steadily. The growth has
instead been concentrated into a series of spurts of activity.
Following the traditions of this occasion, my task this afternoon is to
describe the latest of these periods of discovery, and to tell you of the devel
opment of the tools and techniques that made it possible. Most of us who
become experimental physicists do so for two reasons; we love the tools of
physics because to us they have intrinsic beauty, and we dream of finding
new secrets of nature as important and as exciting as those uncovered by
our scientific heroes. But we walk a narrow path with pitfalls on either side.
If we spend all our time developing equipment, we risk the appellation of
« plumber », and if we merely use the tools developed by others, we risk the
censure of our peers for being parasitic. For these reasons, my colleagues
and I are grateful to the Royal Swedish Academy of Science for citing both
aspects of our work at the Lawrence Radiation Laboratory at the University
of California — the observations of a new group of particles and the creation
of the means for making those observations.
As a personal opinion, I would suggest that modern particle physics started
in the last days of World War II, when a group of young Italians, Conversi,
Pancini, and Piccioni, who were hiding from the German occupying forces,
initiated a remarkable experiment. In 1946, they showed [3] that the
« mesotron », which had been discovered in 1937 by Neddermeyer and Ander
son [4] and by Street and Stevenson [5], was not the particle predicted by
(*) Nobel Lecture, December 11, 1968. Copyright © The Nobel Foundation 1969.
2 L. W. Alvarez
Yukawa [6] as the mediator of nuclear forces, but was instead almost com
pletely unreactive in a nuclear sense. Most nuclear physicists had spent the
war years in militaryrelated activities, secure in the belief that the Yukawa
mesons was available for study as soon as hostilities ceased. But they were
wrong.
The physics community had to endure less than a year of this nightmarish
state; Powell and his collaborators [7] discovered in 1947 a singly charged
particle (now known as the pion) that fulfilled the Yukawa prediction, and
that decayed into the « mesotron », now known as the muon. Sanity was
restored to particle physics, and the pion was found to be copiously produced
in Ernest Lawrence's 184inch cyclotron, by Gardner and Lattes [8] in 1948.
The cosmic ray studies of Powell's group were made possible by the elegant
nuclear emulsion technique they developed in collaboration with the Ilford
laboratories under the direction of C. Waller.
In 1950, the pion family was filled out with its neutral component by
three independent experiments. In Berkeley, at the 184inch cyclotron, Moyer,
York, et al. [9] measured a Dopplershifted yray spectrum that could only
be explained as arising from the decay of a neutral pion, and Steinberger,
Panofsky and Steller [10] made the case for this particle even more convincing
by a beatiful experiment using McMillan's new 300 MeV synchrotron. And
independently at Bristol, Ekspong, Hopper, and King [11] observed the two
yray decay of the n° in nuclear emulsion, and showed that its lifetime was
less than 510~ 14 s.
In 1952 Anderson, Fermi, and their collaborators [12] at Chicago started
their classic experiments on the pionnucleon interaction at what we would
now call low energy. They used the external pion beams from the Chicago
synchrocyclotron as a source of particles, and discovered what was for a long
time called the pionnucleon resonance. The isotopic spin formalism, which
had been discussed for years by theorists since its enunciation in 1936 by
Cassen and Condon [13], suddenly struck a responsive chord in the experi
mental physics community. They were impressed by the way Brueckner [14]
showed that « /spin » invariance could explain certain ratios of reaction
crosssections, if the resonance, which had been predicted many years earlier
by Pauli and Dancoff [15] were in the f isotopic spin state, and had an angular
momentum of f .
By any test we can now apply, the « 3,3 resonance » of Anderson, Fermi
et al. was the first of the « new particles » to be discovered. But since the rules
for determining what constitutes a discovery in physics have never been
codified — as they have been in patent law — it is probably fair to say that
it was not customary, in the days when the properties of the 3,3 resonance
were of paramount importance to the high energy physics community, to
Recent developments in particle physics 3
regard that resonance as a « particle ». Neutron spectroscopists study hun
dreds of resonances in neutronnucleus system which they do not regard
as separate entities, even though their lives are billions of times as long.
I don't believe that an early and general recognition that the 3,3 resonance
should be listed in the « table of particles » would in any way have speeded
up the development of high energy physics.
Although the study of the production and the interaction of pions had
passed in a decisive way from the cosmic ray groups to the accelerator labora
tories in the late 1940's, the cosmicrayoriented physicists soon found two
new families of « strange particles » — the K mesons and the hyperons. The
existence of the strange particles has had an enormous inpact on the work
done by our group at Berkeley. It is ironic that the parameters of the Beva
tron were fixed and the decision to build that accelerator had been made
before a single physicist in Berkeley really believed in the existence of strange
particles. But as we look back on the evidence, it is obvious that the observa
tions were well made, and the conclusions were properly drawn. Even if we
had accepted the existence — an more pertinently the importance — of these
particles, we would not have known what energy the Bevatron needed to
produce strange particles; the associated production mechanism of Pais [16]
and its experimental proof by Fowler, Shutt et al. [17] were still in the future.
So the fact that, with a few notable exceptions, the Bevatron has made its
greatest contributions to physics in the field of strange particles must be
attributed to a very fortunate set of accidents.
The Bevatron's proton energy of 6.3 GeV was chosen so that it would
be able to produce antiprotons, if such particles could be produced. Since,
in the interest of keeping the « list of particles » tractable, we no longer count
antiparticles nor individual members of /spin multiplets, it is becoming
fashionable to regard the discovery of the antiproton as an « obvious exercise
for the student ». (If we were to apply the « new rules » to the classical work
of Chadwick and Anderson, we would conclude that they hadn't done anything
either — the neutron is simply another /spin state of the proton, and Ander
son's positron is simply the obvious antielectron !) In support of the non
obvious nature of the Segre group's discovery of the antiproton [18] I need
only recall that one of the most distinguished high energy physicists I know,
who didn't believe that antiprotons could be produced, was obliged to settle
a 500dollar bet with a colleague who held the now universally accepted
belief that all particles can exist in an antistate.
I have just discussed in a very brief way the discovery of some particles
that have been of importance in our bubble chamber studies, and I will
continue the discussion throughout my lecture. This account should not be
taken to be authoritative — there is no authority in this area — but simply
4 L. W. Alvarez
as a narrative to indicate the impact that certain experimental work had
on my own thinking and on that of my colleagues.
I will now return to the story of the very important strange particles.
In contrast to the discovery of the pion, which was accepted immediately
by almost everyone — one apparent exception will be related later in this talk —
the discovery and the eventual acceptance of the existence of the strange
particles stretched out over a period of a few years. Heavy, unstable particles
were first seen in 1947, by Rochester and Butler [19], who photographed
and properly interpreted the first two « V particles » in a cosmicraytriggered
cloud chamber. One of the V's was charged, and was probably a K meson.
The other was neutral, and was probably a K°. For having made these
observations, Rochester and Butler are generally credited with the discovery
of strange particles. There was a disturbing period of two years in which
Rochester and Butler operated their chamber and no more V particles were
found. But in 1950 Anderson, Leighton et al. [20] took a cloud chamber
to a mountain top and showed that it was possible to observe approximately
one V particle per day under such conditions. They reported, « To interpret
these photographs, one must come to the same remarkable conclusion as that
drawn by Rochester and Butler on the basis of these two photographs, viz.,
that these two types of events represent, respectively, the spontaneous decay
of neutral and charged unstable particles of a new type ».
Butler and his collaborators then took their chamber to the PicduMidi
and confirmed the high event rate seen by the CalTech group on White
Mountain. In 1952 they reported the first cascade decay [21] — now known
as the E~ hyperon.
While the cloud chamber physicists were slowly making progress in under
standing the strange particles, a parallel effort was under way in the nuclear
emulsionoriented laboratories. Although the first K meson was undoubtedly
observed in LeprinceRinguet's cloud chamber [22] in 1944, Bethe [23] cast
sufficient doubt on its authenticity that it had no influence on the physics
community and on the work that followed. The first overpowering evidence
for a K meson appeared in nuclear emulsion, in an experiment by Brown
and most of the Bristol group [24], in 1949. This socalled t + meson decayed
at rest into three coplanar pions. The measured ranges of the three pions
gave a very accurate mass value for the t meson of 493.6 MeV. Again there
was a disturbing period of more than a year and a half before another t meson
showed up.
In 1951, the year after the t meson and the V particles were finally seen
again, O'Ceallaigh [25] observed the first of his kappa mesons in nuclear
emulsion. Each such event involved the decay at rest of a heavy meson into
a muon with a different energy. We now know these particles as K + mesons
Recent developments in particle physics 5
decaying into fx + +7c°+v, so the explanation of the broad muon energy
spectrum is now obvious. But it took some time to understand this in the
early 1950's, when these particles appeared one by one in different laboratories.
In 1953, Menon and O'Ceallaigh [26] found the first K^ or 8 meson, with
a decay into ~ + +tt . The identification of the 6 and t mesons as different
decay modes of the same K mesons is one of the great stories of particle
physics, and it will be mentioned later in this lecture.
The identification of the neutral A emerged from the combined efforts
of the cosmic ray cloud chamber groups, so I will not attempt to assign
credit for its discovery. But it does seem clear that Thompson et ah [27]
were the first to establish the decay scheme of what we now know as the K?
meson: Ki^tc++7tT. The first example of a charged 21 hyperon was seen
in emulsion by the Genoa and Milan group [28], in 1953. And after that,
the study of strange particles passed, to a large extent, from the cosmic ray
groups to the accelerator laboratories.
So by the time the Bevatron first operated, in 1954, a number of different
strange particles had been identified ; several charged particles and a neutral
one all with masses in the neighborhood of 500 MeV, and three kinds of
particles heavier than the proton. In order of increasing mass, these were
the neutral A, the two charged 2's (plus and minus), and the negative cascade
(E~), which decayed into a A and a negative pion.
The strange particles all had lifetimes shorter than any known particles
except the neutral pion. The hyperons all had lifetimes of approximately
10~ 10 s, or less than 1 % of the charged pion lifetime. When I say that
they were called strange particles because their observed lifetimes presented
such a puzzle for theoretical physicists to explain, I can imagine the lay
members in this audience saying to themselves, « Yes, I cannot see how
anything could come apart so fast. » But the strangeness of the strange
particles is not that they decay so rapidly, but that they last almost a million
million times longer than they should — physicists could not explain why
they did not come apart in about 10~ 21 s.
I will not go into the details of the dilemma, but we can note that a similar
problem faced to physics community when the muon was found to be so
inert, nuclearly. The suggestion by Marshak and Bethe [29] that it was the
daughter of a strongly interacting particle was published almost simultane
ously with the independent experimental demonstration by Powell et ah
mentioned earlier. Although invoking a similar mechanism to bring order
into the strangeparticle arena was tempting, Pais [16] made his suggestion
that strange particles were produced « strongly » in pairs, but decayed
« weakly » when separated from each other.
GellMann [30] (and independently Nishijima [31] then made the first
6 L. W. Alvarez
of this several major contributions to particle physics by correctly guessing
the rules that govern the production and decay of all the strange particles.
I use the word « guessing » with the same sense of awe I feel when I say that
Champollion guessed the meanings of the hieroglyphs on the Rosetta Stone.
GellMann had first to assume that the K meson was not an /spin triplet,
as it certainly appeared to be, but an /spin doublet plus is antiparticles, and
he had further to assume the existence of the neutral 2 and fo the neutral E.
And finally, when he assigned appropriate values of his new quantum
number, strangeness, to each family, his rules explained the one observed
production reaction and predicted a score of others. And of course it
explained all the known decays, and predicted another. My research group
eventually confirmed all of GellMann's and Nishijima's early predictions,
many of them for the first time, and we continue to be impressed by their
simple elegance.
This was the state of the art in particle physics in 1954, when William
Brobeck turned his brainchild, the Bevatron, over to his Radiation Laboratory
associates to use as a source of high energy protons. I has been using the
Berkeley proton linear accelerator in some studies of shortlived radioactive
species, and I was pleased at the chance to switch to a field that appeared to
be more interesting. My first Bevatron experiment was done in collaboration
with Sula Goldhaber [32] ; it gave the first real measurement of the t meson
lifetime. My next experiment was done with three talented young post
doctoral fellows, Frank S. Crawford jr., Myron L. Good and M. Lynn
Stevenson. An early puzzle in Kmeson physics was that two of the particles
(the 6 and t) had similar, but poorly determined lifetimes and masses. That
story has been told in this auditorium by Lee [33] and Yang [34] so I will
not repeat it now. But I do like to think that our demonstration [35], simul
taneously with and independently from one by Fitch and Motley [36], that
the two lifetimes were not measurably different, plus similar small limits on
possible mass differences set by von Friesen et al. [37] and by Birge et al. [38],
nudged Lee and Yang a bit toward their revolutionary conclusion.
Our experiences with what was then a very complicated array of scintilla
tion counters led me and my colleagues to despair of making meaningful
measurements of what we perceived to be the basic reactions of strange particle
physics :
7i+p >A + K°
I I
the production reaction is indicated by the horizontal arrows, the subsequent
decays by the vertical arrows. Figure 1 shows a typical example of this reac
Recent' developments in particle physics
Fig. J.
+»* K"+A.
tion, as we saw it later in the 10 in. bubble chamber. We concluded, correctly
I believe, that none of the then known techniques was well suited to study
this reaction. Counters appeared hopelessly inadequate to the task, and the
spark chamber had not yet been invented. The Brookhaven diffusion cloud
chamber group [17] had photographed only a few events like shown in
Fig. I, in a period of two years. It seemed to us that a trackrecording
technique was called for, but each of the three known track devices had
drawbacks that ruled it out as a serious contender for the role we envisaged.
Nuclear emulsion, which had been so spectacularly successful in the hands
of Powell's group, depended on the contiguous nature of the successive tracks
at a production or decay vertex. The presence of neutral and therefore non
ionizing particles between related charged particles, plus lack of even a rudi
mentary time resolution, made nuclear emulsion techniques virtually unusable
in this new field. The two known types of cloud chambers appeared to have
equally insurmountable difficulties. The older Wilson expansion chamber
had two difficulties that rendered it unsuitable for the job: if used at atmos
pheric pressure, its cycling period was measured in minutes, and if one
increased its pressure to compensate for the long mean free path of nuclear
interactions, its cycling period increased at least as fast as the pressure was
increased. Therefore the number of observed reactions per day started at
8 L. W. Alvarez
an almost impossibly low value, and dropped as « corrective action » was
taken. The diffusion cloud chamber was plagued by « background problems »,
and had an additional disadvantage — its sensitive volume was confined in
the vertical direction to a height of only a few centimeters. What we conclude
from all this was simply that particle physicists needed a trackrecording device
with solid or liquid density (to increase the rate of production of nuclear
events by a factor of 100), with uniform sensitivity (to avoid the problems
of the sensitive layer in the diffusion chamber), and with fast cycling time
(to avoid the Wilson chamber problems). And of course, any cycling detector
would permit the association of charged tracks joined by neutral tracks,
which was denied to the user of nuclear emulsion.
In late April of 1953 I paid my annual visit to Washington, to attend the
meeting of the American Physical Society. At lunch of the first day, I found
myself seated at a large table in the garden of the Shoreham Hotel. All the
seats but one were occupied by old friends from World War II days, and we
reminisced about our experiences at the MIT radar laboratory and at Los
Alamos. A young chap who had not experienced those exciting days was
seated at my left, and we were soon talking of our interests in physics. He
expressed concern that no one would hear his 10 min contributed paper,
because it was scheduled as the final paper of the Saturday afternoon ses
sion, and therefore the last talk to be presented at the meeting. In those
days of slow airplanes, there were even fewer people in the audience for the
last paper of the meeting than there are now — if that is possible. I admitted
that I would not be there, and asked him to tell me what he would be reporting.
And that is how I heard first hand from Donald Glaser how he had invented
the bubble chamber, and to what state he had brought its development.
And of course he has since described those achievements from this plat
form [39]. He showed me photographs of bubble tracks in a small glass
bulb, about 1 cm in diameter and 2 cm long, filled with diethyl ether. He
stressed the need for absolute cleanliness of the glass bulb, and said that
he could maintain the ether in a superheated state for an average of many
seconds before spontaneous boiling took place. I was greatly impressed by
his work, and it immediately occurred to me that this could be the « big
idea » I felt was needed in particle physics.
That night in my hotel room I discussed what I had learned with my col
league from Berkeley, Frank Crawford. I told Frank that I hoped we could
get started on the development of a liquid hydrogen chamber, much larger
than anything Don Glaser was thinking about, as soon as I returned to Berke
ley. He volunteered to stop off in Michigan on the way back to Berkeley,
which he did, and learned everything he could about Glaser's technique.
I returned to Berkeley on Sundary, May 1, and on the next day Lynn
Recent developments in particle physics 9
Stevenson started to keep a new notebook on bubble chambers. The other day,
when he saw me writing this talk, he showed me that old notebook with its
first entry dated May 2, 1953, with Van der Waal's equation on the first
page, and the isotherms hydrogen traced by hand onto the second page.
Frank Crawford came home a few days later, and he and Lynn moved into
the « student shop » in the synchrotron building, to build their first bubble
chamber. They were fortunate in enlisting the help of John Wood who was
an accelerator technician at the synchrotron. The three of them put their
first efforts into a duplication of Glaser's work with hydrocarbons. When they
has demonstrated radiation sensitivity in ether, they built a glass chamber in
a Dewar flask to try first with liquid nitrogen and then with liquid hydrogen.
I remember that on several occasions I telephoned to the late Earl Long
at the University of Chicago, for advice on cryogenic problems. Dr. Long
gave active support to the liquid hydrogen bubble chamber that was being
built at that time by Roger Hildebrand and Darragh Nagle at the Fermi
Institute in Chicago. In August of 1953 Hildebrand and Nagle [40] showed
that superheated hydrogen boiled faster in the presence of a gammaray source
than it did when the source was removed. This is a necessary (though not
sufficient) condition for successful operation of a liquid hydrogen bubble
chamber, and the Chicago work was therefore an important step in the devel
opment of such chambers. The important unanswered question concerned
the bubble density— was it sufficient to see tracks of « minimum ionizing »
particles, or did liquid hydrogen — as my colleagues had just shown that
liquid nitrogen did — produce bubbles but no visible tracks?
John Wood saw the first tracks in a 1.5 in.diameter liquid hydrogen bub
ble chamber in February of 1954 [41]. The Chicago group could certainly
have done so earlier, by rebuilding their apparatus, but they switched their
efforts to hydrocarbon chambers, and were rewarded by being the first physi
cists to publish experimental results obtained by bubble chamber techniques.
Figure 2 is a photograph of Wood's first tracks.
At the Lawrence Radiation Laboratory, we have long had a tradition of
close cooperation between physicists and technicians. The resulting at
mosphere, which contributed so markedly to the rapid development of the
liquid hydrogen bubble chamber, led to an unusual phenomenon: none of the
scientific papers on the development of bubble chamber techniques in my
research group were signed by experimenters who were trained as physicists
or who had had previous cryogenic experience. The papers all had authors
who were listed on the Laboratory records as technicians, but of course the
physicists concerned knew what was going on, and offered many suggestions.
Nonetheless, our technical associates carried the main responsibility, and
published their findings in the scientific literature. I believe this is a healthy
10 L. W. Alvarez
Fig. 2. First tracks in hydrogen.
change from practices thai were common a generation ago; we all remember
papers signed by a single physicist that ended with a paragraph saying, « 1 wish
to thank Mr. , who built the apparatus and took much of the
data ».
And speaking of acknowledgments, John Wood's first publication, in ad
dition to thanking Crawford, Stevenson, and me for our advice and help, said,
«1 am indebted to A. J. Schwcmin for help with the electronic circuits ».
« Pete » Schwemin, the most versatile technician I have ever known, became
so excited by his initial contact with John Wood's 1.5 in. diameter allglass
chamber tluit he immediately started the construction of" the first metal
bubble chamber with glass windows. All earlier chambers had been made
completely of smooth glass, without joints, to prevent accidental boiling at
sharp points; such boiling of course destroyed the superheat and made the
chamber insensitive to radiation. Both Glaser and Hildcbrami stressed the
long times their liquids could be held in the superheated condition; Hilde
brand and Nagle averaged 22 s and observed one superheat period of 70 s.
John Wood reported [41], « Wc were discouraged by our inability to attain
the long times of superheat, until the track photographs showed that it was
not important in the successful operation of a large bubble chamber ». 1 have
always felt that second to Glaser's discovery of tracks this was the key
Recent developments in particle physics 1 1
observation in the whole development of bubble chamber technique. As long
as one « expanded the chamber » rapidly, bubbles forming on the wall didn't
destroy the superheated condition of the main volume of the liquid, and it
remained sensitive as a trackrecording medium.
Pete Schwemin, with the help of Douglas Parmentier [42], built the 2.5 in.
diameter hydrogen chamber in record time, as the world's first « dirty cham
ber ». I have never liked that expression, but it was used for a while to
distinguish chambers with windows gasketed to metal bodies from allglass
chambers. Because of it « dirtiness », the 2.5 in. chamber boiled at its walls,
but still showed good tracks throughout its volume. Now that « clean »
chambers are of historical interest only, we can be pleased that the modern
chambers need no longer be stigmatized by the adjective « dirty ».
Lynn Stevenson's notebook shows a diagram of John Wood's chamber
dated January 25, 1954, with Polaroid pictures of tracks in hydrogen. A
month later he recorded details of Schwemin's 2.5 in. chamber, and drew
a complete diagram dated March 5. (That was the day after the Physical
Review received Wood's letter announcing the first observation of tracks.)
On April 29, Schwemin and Parmentier photographed their first tracks ; these
are shown in Fig. 3. (Things were happening so fast at this time that the
2.5 in. system was never photographed as a whole before it ended up on the
scrap pile.)
In August, Schwemin and Parmentier separately built two different 4 in.
diameter chambers. Both were originally expanded by internal bellows, and
Parmentier's 4 in. chamber gave tracks on October 6. Schwemin's chamber
produced tracks three weeks later, and survived as the 4 in. chamber. (See
Fig. 4.) The bellows systems in both chambers failed, but it turned out to be
easier to convert Schwemin's chamber to the vapor expansion system that
was used in all our subsequent chambers until 1962. (In that year, the 25 in.
chamber introduced the « Q bellow » that is now standard for large chambers.)
Figure 5 shows all our chambers displayed together a few weeks ago, at
the request of Swedish Television. As you can see, we all look pretty pleased
to see so many of our « old friends » side by side for the first time.
Figure 6 shows an early picture of multiple meson production in the 4 in.
chamber. This chamber was soon equipped with a pulsed magnetic field, and
in that configuration it was the first bubble chamber of any kind to show
magnetically curved tracks. It was then set aside by our group as we pushed
on to larger chambers. But it ended its career as a useful research tool at
the Berkeley electron synchrotron, after almost two million photographs of
300 MeV bremsstrahlung passing through it had been taken and analyzed
by Bob Kenney et al. [43].
In the year 1954, as I have just recounted, various members of my research
12
L, W, Akcrei
I
Recent deicfojments in par tick physics 13
Fig, 4.  4 in, chamber, D, Parmenlier (left), A, J, Sehwemrn (right),
group had been responsible for the successful operation of four separate
liquid hydrogen bubble chambers, increasing in diameter from 15 to 4 in.
By the end of that eventful year, it was clear that it would take a more con
certed engineeringtype approach to the problem if we were to progress to the
larger chambers we felt were essential to the solution of highenergy physics
problems. 1 therefore enlisted the assistance of three close associates, J. Donald
Gow, Robert Walt and Richard Bluniberg. Don Gow and Bob Watt had
14
L. W. Alvarez
Fig. 5.  Display of chambers, November 1968. Prom left to right, 1^, 4, 6,
10, 15 and 72 in. chambers; Hernandez, Schwemin, Rinla, Watt,, Alvarez and
Eckman,
taken over full responsibility for the development and operation of the
32 McV linear accelerator that had occupied ail my attention from its inception
late in 1945 until it first operated in late 1947. Neither of them had any
experience with cryogenic techniques, but they learned rapidly, and were soon
leaders in the new technology of hydrogen bubble chambers. Dick Blum berg
had been trained as a mechanical engineer, and he had designed the equip
ment used by Crawford, Stevenson and me in our experiments, then in pro
gress, on the Compton scattering of yrays by protons [44].
Wilson Powell had built two large magnets to accommodate his Wilson
Cloud Chambers, pictures from which adorned the walls of every cyclotron
laboratory in the world. He very generously plaeed one of these magnets at
our disposal, and Dick. Blum berg immediately started the mechanical design
of the 10 in. chamber— the largest size we felt could be accommodated in
the well of Powell's magnet, Blumberg's drafting table was in the middle of
the single room that contained the desks of all the members of my research
group. Not many engineers will tolerate such working conditions, but Blum
berg was able to do so and he produced a design that was quickly built in
the main machine shop. All earlier chambers had been built by the exper
imenters themselves. The design of the 10 in. chamber turned out to be a
much larger job than we had foreseen. By the time it was completed, eleven
members of the Laboratory's Mechanical Engineering Department had worked
on it, including Rod Byrns and John Mark. The electrical engineering aspects
of all our large chambers were formidable, and we are indebted to Jim Shand
for his leadership in this work for many years.
Recent developments in particle physics
15
Fig, 6,  Multiple meson production in 4 in. chamber.
Great difficulty was experienced with the first operation of the 10 in.
chamber; too much hydrogen was vaporized at each « expansion ». Pete
Schwemin quickly diagnosed the trouble and built a fastacting valve that
permitted the chamber to be pulsed every 6 s, to match (lie Bevatron's
cycling time.
It would be appropriate to interrupt this description of the bubble chamber
development program to describe the important observations made possible
by the operation of the 10 in. chamber early in 1956, but instead, I will
preserve the continuity by describing the further development of the hardware.
In December of 1954, shortly after the 4 in. chamber had been operated in
the cyclotron building for the first time, it became evident to me that the
10 in. chamber we bad just started to design would not be nearly large
enough to tell us what we wanted to know about the strange particles. The
tracks of these objects had been photographed at Brookhaven [17], and we
knew they were produced copiously by the Bevatron,
16 L. W. Alvarez
The size of the « big chamber » was set by several different criteria, and
fortunately all of them could be satisfied by one design. (Too often, a designer
of new equipment finds that one essential criterion can be met only if the
object is very large, while an equally important criterion demands that it
be very small.) All « dirty chambers » so far built throughout the world had
been cylindrical in shape, and were characterized by their diameter measure
ment. By studying the relativistic kinematics of strange particles produced by
Bevatron beams, and more particularly by studying the decay of these par
ticles, I convinced myself that the big chamber should be rectangular, with a
length of at least 30 in. This length was next increased to 50 in. in order that
there would be adequate amounts of hydrogen upstream from the required
decay region, in which production reactions could take place. Later the length
was charged to 72 in. , when it was realized that the depth of the chamber
could properly be less than its width and that the change could be made
without altering the volume. The production region corresponded to about
10% of a typical pionproton mean free path, and the size of the decay region
was set by the relativistic timedilated decay lengths of the strange particles,
plus the requirement that there be a sufficient track length available in which
to measure magnetic curvature in a « practical magnetic field » of 15000 G.
In summary, then, the width and depth of the chamber came rather simply
from an examination of the shape of the ellipses that characterize relativistic
transformations at Bevatron energies, plus the fact that the magnetic field
spreads the particles across the width but not along the 'depth of the chamber.
The result of this straightforward analysis was a rather frightening set of
numbers: The chamber length was 72 in.; its width was 20 in., and its
depth was 15 in. It had to be pervaded by a magnetic field of 15000 G,
so its magnet would weigh at least 100 tons and would require 2 or 3 MW
to energize it. It would require a window 75 in. long by 23 in. wide and 5 in.
thick to withstand the (deuterium) operating pressure of 8 atm, exerting a
force of 100 tons on the glass. No one had any experience with such large
volumes of liquid hydrogen; the hydrogenoxygen rocket eingines that now
power the upper stages of the Saturn boosters were still gleams in the eyes
of their designers — these were preSputnik days. The safety aspects of the
big chamber were particularly worrisome. Low temperature laboratories had
a reputation for being dangerous places in which to work, and they did not
deal with such large quantities of liquid hydrogen, and what supplies they
did use were kept at atmospheric pressure.
For some time, the glass window problem seemed insurmountable — no
one had ever cast and polished such a large piece of optical glass. Fortunately
for the eventual success of the project, I was able to persuade myself that
the chamber body could be constructed of a transparent plastic cylinder with
Recent developments in particle physics 17
metallic end plates. This notion was later demolished by my engineering
colleagues, but it played an important role in keeping the project alive in
my own mind until I was convinced that the glass window could be built.
As an indication of the cryogenic « state of the art » at the time we worried
about the big window, I can recall the following anecdote. One day, while
looking through a list of titles of talks at a recent cryogenic conference, I
spotted one that read, « Large glass window for viewing liquid hydrogen ».
Eagerly I turned to the paper — but it described a metallic Dewar vessel
equipped with a glass window 1 in. in diameter!
Don Gow was now devoting all his to hydrogen bubble chambers, and
in January of 1955 we interested Paul Hernandez in taking a good hard
engineering look at the problems involved in building and housing the 72 in.
bubble chamber. We were also extremely fortunate in being agle to interest the
cryogenic engineers at the Boulder, Colorado, branch of the National Bureau
of Standards in the project. Dudley Chelton, Bascomb Birmingham and Doug
Mann spent a great deal of time with us, first educating us in largescale
liquid hydrogen techniques, and later cooperating with us in the design and
initial operation of the big chamber.
In April of 1955, after several months of discussion of the large chamber,
I wrote a document entitled The Bubble Chamber Program at UCRL. This
paper showed in some detail why it was important to build the large chamber,
and outlined a whole new way of doing highenergy physics with such a device
It stressed the need for semiautomatic measuring devices (which had not
previously been proposed), and described how electronic computers would
reconstruct tracks in space, compute momenta, and solve problems in rela
tivistic mechanics. All these techniques are now part of the « standard bubble
chamber method », but in April of 1955 no one had yet applied them. Of all
the papers I have written in my life, none gives me so much satisfaction on
rereading as does this unpublished prospectus.
After Paul Hernandez and Don Gow has estimated that the big chamber,
including its building and power supplies, would cost about 2.5 million dollars,
it was clear that a special AEC appropriation was required; we could no
longer build our chambers out of ordinary laboratory operating money. In
fact, the document I have just described was written as a sort of proposal
to the AEC for financial support — but without mentioning money! I asked
Ernest Lawrence if he would help me in requesting extra funds from the
AEC. He read the document, and agreed with the points I had made. He
then asked me to remind him of the size of the world's largest hydrogen
chamber. When I replied that it was 4 in. in diameter, he said the though I
was making too large an extrapolation in one step, to 72 in. I told him that
the 10 in. chamber was on the drawing board, and if we could make it work,
18 L. W. Alvarez
the operation of the 72 in. chamber was assured. (And if we could not make
it work, we could refund most of the 2.5 million.) This was not obvious
until I explained the hydraulic aspects of the expansion system of the 72 in.
chamber; it was arranged so that the 20 in. wide, 72 in. long chamber could
be considered to be a large collection of essentially independently expanded
10 in. square chambers. He was not convinced of the wisdom of the pro
gram, but in a characteristic gesture, he said, « I don't believe in your big
chamber, but I do believe in you, and I'll help you to obtain the money ».
I therefore accompanied him on his next trip to Washington, and we talked
in one day to three of the five Commissioners: Lewis Strauss, Willard Libby
(who later spoke from this podium), and the late John von Neumann, the
greatest mathematical physicist then living. That evening, at a cocktail party
at Johnny von Neumann's home, I was told that the Commission had voted
that afternoon to give the laboratory the 2.5 million dollars we had requested.
All we had to do now was build the thing and make it work!
Design work had of course been under way for some time, but it was
now rapidly accelerated. Don Gow assumed a new role that is not common in
physics laboratories, but is well known in military organizations; he became
my « chief of staff ». In this position, he coordinated the efforts of the phys
icists and engineers; he had full responsibility for the careful spending of our
precious 2.5 million dollars, and he undertook to become an expert second
to none in all the technical phases of the operation, from low temperature
thermodynamics to safety engineering. His success in this difficult task can
be recognized most easily in the success of the whole program, culminating
in the fact that I am speaking here this afternoon. I am sorry that Don Gow
can not be here today; he died several years ago, but I am reminded of him
every day — my threeyearold son is named Donald in his memory.
The engineering team under Paul Hernandez's direction proceeded rapidly
with the design, and in the process solved a number of difficult problems
in ways that have become standard « in the industry ». A typical problem
involved the very considerable differential expansion between the stainless
steel chamber and the glass window. This could be lived with in the 10 in.
chamber, but not in the 72 in. Jack Franck's « inflatable gasket » allowed
the glass to be seated against the chamber body only after both had been
cooled to liquid hydrogen temperature.
Just before leaving for Stockholm, I attended a ceremony at which Paul
Hernandez was presented with a trophy honoring him as a « Master Designer »
for his achievements in the engineering of the 72 in. chamber. I had the
pleasure of telling in more detail than I can today of his many contributions
to the success of our program. One of his associates recalled a special service
that he rendered not only to our group but to all those who followed us in
Recent developments in particle physics 19
building liquid hydrogen bubble chambers. Hernandez and his associates
wrote a series of Engineering Notes, on matters of interest to designers of
hydrogen bubble chambers, that soon filled a series of notebooks that spanned
3 ft of shelf space. Copies of theses were sent to all interested parties on both
sides of the Atlantic, and I am sure that they resulted in a cumulative savings
to all bubble chamber builders of several million dollars ; had not all this infor
mation been readily available, the test programs and calculations of our
engineering group would have required duplication at many laboratories,
at a large expense of money and time. Our program moved so rapidly that
there was never time to put the Engineering Notes into finished form for pub
lication in the regular literature. For this reason, one can now read review
articles on bubble chamber technology, and be quite unaware of the part
that our Laboratory played in its development. There are no references to
papers by members of our group, since those papers were never written — the
data that would have been in them had been made available to everyone who
needed them at a much earlier date.
And just to show that I was also deeply involved in the chamber design,
I might recount how I purposely « designed myself into a corner » because I
thought the result were important, and I thought I could invent a way out
of a severe difficulty, if given the time. All previous chambers had had two
windows, with « straight through » illumination. Such a configuration reduces
the attainable magnetic field, because the existence of a rear pole piece would
interfere with the lightprojection system. I made the decision that the 72 in.
chamber would have only a top window, thereby permitting the magnetic
field to be increased by a lower pole piece and at the same time saving the
cost of the extra glass window, and also providing added safety by eliminating
the possibility that liquid hydrogen could spill through a broken lower window.
The only difficulty was that for more than a year, as the design was firmed
up and the parts were fabricated, none of us could invent a way both to
illuminate and to photograph the bubbles through the same window. Duane
Norgren, who has been responsible for the design of all our bubble chamber
cameras, discussed the matter with me at least once a week in that critical
year, and we tried dozens of schemes that did not quite do the job. But as a
result of our many failures, we finally came to understand all the problems,
and we eventually hit on the retrodirecting system known as coat hangers.
This solution came none too soon ; if it had been delayed by a month or more,
the initial operation of the 72 in. chamber would have been correspondingly
delayed. We took many other calculated risks in designing the system; if
we had postponed the fabrication of the major hardware until we had solved
all the problems on paper, the project might still not be completed. Engineers
are conservative people by nature; it is the ultimate disgrace to have a boiler
20 L. W. Alvarez
explode or a bridge collapse. We were therefore fortunate to have Paul
Hernandez as our chief eingineer; he would seriously consider anything his
physics colleagues might suggest, no matter how outlandish it might seem
at first sight. He would firmly reject it if it could not be made safe, but before
rejecting any idea for lack of safety he would use all the ingenuity he pos
sessed to make it safe.
We felt that we needed to build a test chamber to gain experience with a
singlewindow system, and to learn to operate with a hydrogen refrigerator;
our earlier chambers had all used liquid hydrogen as a coolant. We therefore
built and operated the 15 in. chamber in the Powell magnet, in place of the
10 in. chamber that had served us so well.
The 72 in. chamber operated for the first time on March 24, 1959, very
nearly four years from the time it was first seriously proposed. Figure 7 shows
it at about that time. The « startup team » consisted of Don Gow, Paul
Hernandez and Bob Watt, all of whom had played key roles in the initial
operation of the 15 in. chamber. Bob Watt and Glenn Eckman have been
responsible for the operation of all our chambers from the earliest days of
the 10 in. chamber, and the success of the whole program has most often
rested in their hands. They have maintained an absolutely safe operating
record in the face of very severe hazard, and they have supplied their col
leagues in the physics community with approximately ten million highquality
stereo photographs. And most recently, they have shown that they can design
chambers as well as they have operated them. The 72 in. chamber was
recently enlarged to an 82 in. size, incorporating to a large extent the design
concepts of Watt and Eckman.
Although I have not done justice to the contributions of many close friends
and associates who shared in our bubble chamber development program, I
must now turn to another important phase of our activities — the dataanalysis
program. Soon after my 1955 prospectus was finished, Hugh Bradner under
took to implement the semiautomatic measuring machine proposal. He first
made an exhaustive study of commercially available measuring machines,
encoding techniques, etc., and then, with Jack Franck, designed the first
« Franckenstein ». This rather revolutionary device has been widely copied, to
such an extent that objects of its kind are now called « conventional » measur
ing machines (Fig. 8). Our first Franckenstein was operating reliably in 1957,
and in the summer of 1958 a duplicate was installed in the U.S. exhibit at
the « Atoms for Peace » exposition in Geneva. It excited a great deal of
interest in the highenergy physics community, and a number of groups set
out to make similar machines based on its design. Almost everyone thought
at first that our provision for automatic track following was a needless waste
of money, but over the years, that feature has also come to be « conventional ».
Recent developments in particle physics
21
Jack Franck then went on to design the Mark II Franckenstein, to measure
72 in. bubble chamber film. He had the first one ready to operate just in time
to match the rapid turnon of the big chamber, and he eventually built three
Fig. 7.  72 in. bubble chamber in its building.
more of the Mark It's. Other members of our group then designed and
perfected the faster and less expensive SMP system, which added significantly
to our « measuring power ». The moving forces in this development were
Pete Schwemin, Bob Hulsizer, Peter Davey, Ron Ross and Bill Humphrey [45]
22
L. W. Alvarez
Our final and most rewarding effort to improve our measuring ability was
fulfilled several years ago, when our first Spiral Reader became operational.
This single machine has now measured more than one and a half million high
Fig. 8,  « Franckcnstein ».
energy interactions, and has, together with its almost identical twin, measured
one and a quarter million events in the last year. The SAAB Company here
in Sweden is now building and selling Spiral Readers to European laboratories.
The Spiral Reader had a rather checkered career, and it was on several
occasions believed by most workers in the field to have been abandoned by
our group. The basic concept of the spiral scan was supplied by Bruce McCor
mick, In J 956. Our attempts to reduce his ideas to practice resulted in failure,
and shortly after that, McCormick moved to Illinois, where he has since been
engaged in computer development. As the cost of transistorized circuits
dropped rapidly in the next years, we tried a second time to implement the
Spiral Reader concept, using digital techniques to replace the analog devices
of the earlier machine. The second device showed promise, but its « hard
wired logic » made it too inflexible, and the unreliability of its electronic
components kept it in repair most of the time. The mechanical and optical
components of the second Spiral Reader were excellent, and we hated to
drop the whole project simply because the circuitry did not come up to the
Recent developments in particle physics
23
same standard. In 1963, Jack Lloyd suggested that we use one of the new
breed of small highspeed, inexpensive computers to supply the logic and the
control circuits for the Spiral Reader. He then demonstrated great qualities
of leadership by delivering to our research group a machine that has per
formed even better than he had promised it would. In addition to his develop
ment of the hardware, he initiated POOH, the Spiral Reader filtering program,
which was brought to a high degree of perfection by Jim Burkhard. The
smooth and rapid transition of the Spiral Reader from a developmental stage
into a useful operational tool was largely the result of several years of hard
work on the part of Gerry Lynch and Frank Solmitz. Figure 9, from a talk
I gave two and a half years ago [46], shows how the measuring power of our
group has increased over the years, with only a modest increase in personnel.
,000,000
800,000 
600,000
400,000 
q. 200,000 
(/>
c
i2 io o,ooo
80,000
60,000
40,000
20,000 
1 0,000
200.
 100
0) k.
E°
Fig. 9.  Measuring rates.
24 L. W. Alvarez
According to a simple extrapolation of the exponential curve we had been
on from 1957 through 1966, we would expect to be measuring 1.5 million
events per year some time in 1969. But we have already reached that rate
and we will soon be leveling off about there because we have stopped our
development work in this area.
The third key ingredient of our development program has been the
continually increasing sophistication in our utilization of computers, as they
have increased in computational speed and memory capacity. While I can
speak from a direct involvement in the development of bubble chambers and
measuring machines, and in the physics done with those tools, my relationship
to our computer progamming efforts is largely that of an amazed spectator.
We were most fortunate that in 1956 Frank Solmitz elected to join our group.
Although the rest of the group thought of themselves as experimental physicists,
Solmitz had been trained as a theorist, and had shown great aptitude in the
development of statistical methods of evaluating experimental data. When
he saw that our first Franckenstein was about to operate, and no computer
programs were ready to handle the data it would generate, he immediately set
out to remedy the situation. He wrote HYDRO, our first system program for
use on the IBM 650 computer. In the succeeding twelve years he has con
tinued to carry the heavy responsibility for all our programming efforts. A
major breakthrough in the analysis of bubble chamber events was made in the
years 1957 through 1959. In this period, Solmitz and Art Rosenfeld, together
with Horace Taft from Yale University and Jim Snyder from Illinois, wrote
the first « fitting routine », GUTS, which was the core of our first « kinematics
program, KICK ». To explain what KICK did, it is easiest to describe what
physicists had to do before it was written. HYDRO and its successor, PANG,
listed for each vertex the momentum and space angles of the tracks entering
or leaving that vertex, together with the calculated errors in these measure
ments. A physicist would plot the angular coordinates on a stereographic
projection of a unit sphere known as a Wolffplot. If he was dealing with a
threetrack vertex — and that was all we could handle in those days — he
would move the points on the sphere, within their errors, if possible, to make
them coplanar. And of course he would simultaneously change the momentum
values, within their errors, to insure that the momentum vector triangle closed,
and energy was conserved. Since momentum is a vector quantity, the various
conditions could be simultaneously satisfied only after the angles and the
absolute values of the momenta had been changed a number of times in an
iterative procedure. The end result was a more reliable set of momenta and
angles, constrained to fit the conservation laws of energy and momentum.
In a typical case, an experienced physicist could solve only a few Wolffplot
problems in a day. (Lynn Stevenson had written a specific program, COPLAN,
Recent developments in particle physics 25
that solved a particular problem of interest to him that was later handled by
the more versatile GUTS.)
GUTS was being written at a time when one higly respected visitor to the
groups saw the large pile of PANG printout that had gone unanalysed beause
so many of our group members were writing GUTS — a program that was
planned to do the job automatically. Our visitor was very upset at what he
told me was a « foolish deployment of our forces ». He said, « If you would
only get all those people way from their program writing, and put them to
work on Wolffplots, we'd have the answer to some really important physics
in a month or two ». I said I was sure we would end up with a lot more
physics in the next years if my colleagues continued to write GUTS and
KICK. I am sure that those who wrote these pioneering « fitting and kine
matics programs » were subjected to similar pressure. Everyone in the high
energy physics community has long been indebted to these farsighted men
because they knew that what they were doing was right. KICK was soon
developed so that it gave an overall fit to several interconnected vertices,
with various hypothetical identities of the several tracks assumed in a series
of attempts at a fit. The relationship beteen energy and momentum depends
on mass, so a highly constrained fit can be obtained only if the particle
responsible for each track is properly identified. If the degree of constraint
is not so high, more than one « hypothesis » (set of track identifications) may
give a fit, and the physicist must use his judgment in making the identification.
As another example in this alltoobrief sketch of the computational aspects
of our work, I will mention an important program, initiated by Art Rosenfeld
and Ron Ross, that has removed much of the remaining drudgery from the
bubble chamber physicists' life. SUMX is a program that can easily be in
structed to search quickly through large volumes of « kinematics program
output », printing out summaries and tabulations of interesting data. (Like
all our pioneering programs, SUMX was replaced by an improved and more
versatile program— in this case, KIOWA. But I will continue to talk as
though SUMX were still used.) A typical SUMX printout will be a com
puterprinted document 3 in.thick, with hundreds of histograms, scatter
plots, etc.
Hundreds of histograms are similarly printed showing numbers of events
with effective masses for many different combinations of particles, with
various « cuts » on momentum transfer, etc. What all this amounts to is
simply that a physicist is no longer rewarded for his ability in deciding what
histograms he should tediously plot and then examine. He simply tells the
computer to plot all histograms of any possible significance, and then flips
the pages to see which ones have interesting features.
One of my few real interactions with our programming effort came when
26 L. W. Alvarez
I suggested to Gerry Lynch the need for a program he wrote that is known
as GAME. In my work as a nuclear physicist before World War II, I had
often been skeptical of the significance of the « bumps » in histograms, to
which importance was attached by their authors. I developed my own criteria
for judging statistical significance, by plotting simulated histograms, assum
ing the curves to be smooth ; I drew several samples of « Monte Carlo distri
butions », using a table of random numbers as the generator of the samples.
I usually found that my skepticism was well founded because the « faked »
histograms showed as much structure as the published ones. There are of
course many statistical tests designed to help one evaluate the reality of bumps
in histograms, bu in my experience nothing is more convincing than an exam
ination of a set of simulated histograms from an assumed smooth distri
bution.
GAME made it possible, with the aid of a few control cards, to generate
a hundred histograms similar to those produced in any particular experiment.
All would contain the same number of events as the real experiment, and
would be based on a smooth curve through the experimental data. The
standard procedure is to ask a group of physicists to leaf through the 100
histograms — with the experimental histogram somewhere in the pile — and
vote on the apparent significance of the statistical fluctuations that appear.
The first time this was tried, the experimenter — who had felt confident that
his bump was significant — did not know that his own histogram was in the
pile, and did not pick it out as convincing; he picked out two of the computer
generated histograms as looking significant, and pronounced all other —
including his own — as of no significance ! In view of this example, one can
appreciate how many retractions of discovery claims have been avoided in
our group by the liberal use of the GAME program.
As a final example from our program library, I will mention FAKE, which,
like SUMX, has been widely used by bubble chamber groups all over the
world. FAKE, written by Gerry Lynch, generates simulated measurements of
bubble chamber events to provide a method of testing the analysis programs
to determine how frequently they arrive at an incorrect answer.
Now that I have brought you up to date on our parallel developments of
hardware and software (computer programs), I can tell you what rewards we
have reaped, as physicists, from their use. The work we did with the 4 in.
chamber at the 184 in. cyclotron and at the Bevatron cannot be dignified
by the designation « experiments », but it did show examples of tz\iq decay
and neutral strangeparticle decay. The experiences we had in scanning the
4 in. film merely whetted our appetite for the exciting physics we felt sure
would be manifest in the 10 in. chamber, when it came into operation in
Wilson Powell's big magnet.
Recent developments in particle physics 27
Robert Tripp joined the group in 1955, and as his first contribution to
our program he designed a « separated beam » of negative K mesons that
would stop in the 10 in. chamber. We had two different reasons for starting
our bubble chamber physics program with observations of the behavior of
K~ mesons stopping in hydrogen. The first reason involved physics: The
behavior of stopping tz~ mesons in hydrogen had been shown by Panofsky
and his coworkers [47] to be a most fruitful source of fundamental knowledge
concerning particle physics. The second reason was of an engineering nature:
Only one Bevatron « straight section » was available for use by physicists,
and it was in constant use. In order not to interfere with other users, we
decided to set the 10 in. chamber close to a curved section of the Bevatron,
and use secondary particles, from an internal target, that penetrated the wall
of the vacuum chamber and passed between neighboring iron blocks in the
return yoke of the Bevatron magnet. This physical arrangement gave us
negative particles (KT and it~ mesons) of a welldefined low momentum.
By introducing an absorber into the beam, we brought the K~ mesons almost
to rest, but allowed the lighter iz~ mesons to retain a major fraction of their
original momentum. The Powell magnet provided a second bending that
brought the K" mesons into the chamber, but kept the n~ mesons out. That
was the theory of this first separated beam for bubble chamber use. But in
practice, the chamber was filled with tracks of pions and muons, and we
ended up with only one stopped K~ per roll of 400 stereo pairs. It is now
common for experimenters to stop one million K" mesons in hydrogen, in
a single experimental run, but the 137 K~ mesons we stopped in 1956 [48]
gave us a remarkable preview of what has now been learned in the much
longer exposures. We measured the relative branching of K~+p into
S~ + 7i + :2 + 7r:2; + ti :A + tt°.
And in the process, we made a good measurement of the H° mass. We
plotted the first decay curves for the 2+ and S _ hyperons, and we observed for
the first time the interactions of S~ hyperons and protons at rest. We felt
amply rewarded for our years of developmental work on bubble chambers
by the very interesting observations we were now privileged to make.
We had a most exciting experience at this time, that was the result of two
circumstances that no longer obtain in bubble chamber physics. In the first
place, we did all our own scanning of the photographic film. Such tasks are
now carried out by professional scanner, who are carefully trained to recognize
and record « interesting events ». We had no professional scanners at the time
because we would not have known how to train them before this first film
became available. And even if they had been trained, we would not have let
28 L. W. Alvarez
them look at the film— we found it so completely absorbing that there was
always someone standing behind a person using one of our few film viewers,
ready to take over when the first person's eyes tired. The second circumstance
that made possible the accidental discovery I am about to describe was the
very poor quality of our separated K~ beam— by modern standards. Most of
the tracks we observed were made by negative pions or muons, but we also
saw many positively charged particles— protons, pions and muons.
At first we kept no records of any events except those involving strange
particles; we would look quickly at each frame in turn, and shift to the next
one if no « interesting event » showed up. In doing this scanning, we saw
many examples of 7c+[j+e + decays, usually from a pion at rest, and we soon
learned about how long to expect the (a+ track to be— about 1 cm. I did my
scanning on a stereo viewer, so I probably had a better feeling for the length
of a ji+ track in space than did my colleagues, who looked at two projections
of the stero views, sequentially. Don Gow, Hugh Bradner and I often scanned
at the same time, and we showed each other whatever interesting events
came into view. Each of us showed the others examples of what we thought
was an unusual decay scheme: 7t>(jr>e The decay of a [ir at rest into
an e~ in hydrogen, was expected from the early observations by Conversi
et al. [3], but Panofsky et al. [47] had shown that a tz~ meson could not decay
at rest in hydrogen. Our first explanation for our observations was simply
that the pion had decayed just before stopping. But we gradually became
convinced that this explanation really did not fit the facts. There were too
many muons tracks of about the same length, and none that were appreciably
longer or shorter, as the decayinflight hypothesis would predict. We now
began to keep records of these « anomalous decays », as we still called them,
and we found occasional examples in which the muon was horizontal in the
chamber, so its length could be measured. (We had as yet no way of recon
structing tracks in space from two stereo views.) By comparing the measured
length of the negative muon track with that of its more normal positive counter
part, we estimated that the negative muons had an energy of 5.4 MeV,
rather than the wellknown positive muon energy (from positive pion decay
at rest) of 4. 1 MeV. This confirmed our earlier suspicion that the long pri
mary negative track could not be that of a pion, but it left us just as much
in the dark as to the nature of the primary.
After these observations had been made, I gave a seminar describing what
we had observed, and suggesting that the primary might be a previously
unknown weakly interacting particle, heavier than the pion, that decayed into
a muon and a neutral particle, either neutrino or photon. We had just made
the surprising observation, shown in Fig. 10, that there was often a gap, meas
ured in millimeters, between the end of the primary and the beginning of
Recent developments hi particle physics
29
k<
\
• r±~ 4PW ■*.
N '; 1 \
.
V
V ■ * I
^t ^ f: i
. '1 I \ *.
! 1 \
\
s * ■ ■ V
\ v » /*~~^**~
**— ^ C * \ H
i
*,
: • >A v
W' 1 "
Pj T
i
L ' j „^
\ ^^^ '
* i , ■ >
; >
^\
1 "■ 1 *,
; i*i & .
x
' \
' "*\ ! i'
/ A 
\ \ V
•^
\
I
' V4
■ / A
I J •
\
^ . >
/ ' \\ ;
t
* '.
fl V\
* i /
\ \
: ' ■ X .
: V \\
I".
^ . ^ v
■:'"••
' ■• ■ <f
i \
^
• ■■ ■ \
.1 ■ ^
. *. ; ,1 ■ r 
^ \
ii
^ " 1/ Tl J
* \ i ' — \\'
}
\ i l
* i \ :l
\\ »._;,>
i
A •
A
V\
; ' V
\\
\ ?
• \/ V
\ \
■  %
\ ■  . *i
\
K \
} ■ . ' ■ * 1
\
V
■ " \ \
[ v. ...
\
\
Fig. 10.  Muon catalysis (with gap).
the secondary. This finding suggested diffusion by a ratlier longlived negative
particle that orbited around and neutralized one of the protons in the liquid
hydrogen. We had missed many tracks with these « gaps » because no one
has seen such a thing before; we simply ignored such track configurations by
subconsciously assuming that they were unassociated events in a badly clut
tered bubble chamber.
One evening, one of the members of our research team, Harold Ticho from
our Los Angeles campus, was dining with Jack Crawford, a Berkeley astro
physicist he had known when they were students together. They discussed our
observations at some length, and Crawford suggested the possibility that a
fusion reaction might somehow be responsible for the phenomenon. They cal
30 L. W. Alvarez
culated the energy released in several such reactions, and found that it agreed
with experiment if a stopped muon were to be binding together a proton
and a deuteron into an HD firmolecular ion. In such a « mulecule » the
proton and deuteron would be brought into such close proximity for such
a long time that they would fuse into 3 He, and could deliver their fusion
energy to the muon by the process of internal conversion. However, they
could not think of any mechanism that would make the reaction happen so
often — the fraction of deuterons in liquid hydrogen is only 1 in 5000. They
had, however, correctly identified the reaction, but a key ingredient in the
theoretical explanation was still missing.
The next day, when we had all accepted the idea that stopped muons were
catalyzing the fusion of protons and deuterons, our whole group paid a visit
to Edward Teller, at his home. After a short period of introduction to the
observations and to the proposed fusion reaction, he explained the high
probability of the reaction as follows : the stopped muon radiated its way into
the lowest Bohr orbit around a proton. The resulting muonic hydrogen atom,
P(jr, then had many of the properties of a neutron, and could diffuse freely
through the liquid hydrogen. When it came close to the deuteron in an HD
molecule, the muon would transfer to the deuteron, because the ground
state of the yrd atom is lower than that of the (orp atom, in consequence of
« reduced mass » effect. The new « heavy neutron » dyr might then recoil
some distance as a result of the exchange reaction, thus explaining the « gap ».
The final stage of capture of a proton into a pdyc molecular ion was also
energetically favorable, so a proton and deuteron could now be confined
close enough together by the heavy negative muon to fuse into a 3 He nucleus
plus the energy given to the internally converted muon.
We had a short but exhilirating experience when we thought we had solved
all of the fuel problems of mankind for the rest of time. A few hasty calcula
tions indicated that in liquid HD a single negative muon would catalyze enough
fusion reactions before it decayed to supply the energy to operate an accelerator
to produce more muons, with energy left over after making the liquid HD
from sea water. While everyone else had been trying to solve this problem by
heating hydrogen plasmas to millions of degrees, we had apparently stumbled
on the solution, involving very low temperatures instead. But soon, more
realistic estimates showed that we were off the mark by several orders of
magnitude — a « near miss » in this kind of physics !
Just before we published our results [49], we learned that the « [j.catalysis »
reaction had been proposed in 1947 by Frank [50] as an alternative explana
tion of what Powell et al. had assumed (correctly) to be the decay of tt+ to (a+.
Frank suggested that it might be the reaction we had just seen in liquid
hydrogen, starting with a yr, rather than with a tz+. Zel'dovitch [51] had
Recent developments in particle physics
31
extended the ideas of Frank concerning this reaction, but because their
papers were not known to anyone in Berkeley, we had a great deal of personal
pleasure that wc otherwise would have missed.
I will conclude this episode by noting that we immediately increased the
deuterium concentration in our liquid hydrogen and observed the expected,
increase in fusion reactions, and saw two examples of successive catalyses by
a single rnuon (Fig. II). We also observed the catalysis of D+D— > a H  ^H
in pure liquid deuterium.
Fig. II,  Double muon catalysis.
32
L. W. Alvarez
A few months after we had announced our acatalysis results, the world of
particle physics was shaken by the discovery that parity was not conserved
in beta decay. Madame Wu and her collaborators [52], acting on a suggestion
by Lee and Yang [53], showed that the p rays from the decay of oriented
6ft Co nuclei were emitted preferentially in a direction opposite to that of the
spin. Lee and Yang suggested that parity nonconservation might also manifest
itself in the weak decay of the A hyperon into a proton plus a negative pion.
Crawford et at. had moved the 10 in. chamber into a negative pion beam,
and were analysing a large sample of A*S from associated production events.
They looked for an « updown asymmetry » in the emission of pions from
A'Sj relative to the « normal to the production plane », as suggested by Lee
and Yang. As a result, they had the pleasure of being the first to observe
parity nonconservation in the decay of hyperons [54].
Fig. 12.  K~ beam in 72 in. bubble chamber, a) No spectrometers on; b) one
spectrometer on; c) two spectrometers on.
Recent developments in particle physics 33
In the winter of 1958, the 15 in. chamber had completed its engineering
test run as a prototype for the 72 in. chamber, and was operating for the
first time as a physics instrument. Harold Ticho, Bud Good and Philippe
Eberhard [55] had designed and built the first separated beam of K~ mesons
with a momentum of more than 1 GeV/c. Figure 12 shows the appearance
of a bubble chamber when such a beam is passed through it, and when one
or both of the electrostatic separators are turned off. The ingenuity which
has been brought to bear on the problem of beam separation, largely by
Ticho and Murray, is difficult to imagine, and its importance to the success
of our program cannot be overstimated [55]. Joe Murray has recently joined
the Stanford Linear Accelerator Center, where he has in a short period of
time built a very successful radiofrequencyseparated K beam and a back
scattered laser beam.
The first problem we attacked with the 15 in. chamber was that of the H°.
GellMann had predicted that the S~ was one member of an /spin doublet,
with strangeness minus 2. The predicted partner of the H~ would be a neutral
hyperon that decayed into a A and a t? — both neutral particles that would,
like the H°, leave no track in the bubble chamber. A few years earlier, as an
afterdinner speaker at a physics conference, Victor Weisskopf had « brought
down the house » by exhibiting an absolutely blank cloud chamber photo
graph, and saying that it represented proof of the decay of a new neutral
particle into two other neutral particles ! And now we were seriously planning
to do what had been considered patently ridiculous only a few years earlier.
According to the GellMann and Nishijima strangeness rules, the H° should
be seen in the reaction
K~+p^H° + K°
\ \
A+TC° TC _ +TC +
I
In the one example of this reaction that we observed, Fig. 13, the charged
pions from the decay of the neutral K° yielded a measurement of the energy
and direction of the unobserved K°. Through the conservation laws of energy
and momentum (plus a measurement of the momentum of the interacting K~
track) we could calculate the mass of the coproduced S° hyperon plus its
velocity and direction of motion. Similarly, measurements of the if and
proton gave the energy and direction of motion of the unobserved A, and
proved that it did not come directly from the point at which the K~ meson
interacted with the proton. The calculated flight path of the A intersected
the calculated flight path of the H°, and the angle of intersection of the two
34
L. W. Alvarez
Fig, 13.  Production and decay of a neulrat cascade hyperon (E°).
unobserved but calculated tracks gave a confirming measurement of the
mass of the E 1 hyperon, and proved that it decayed into a A plus a 
This single hardwon event was a sort of tour de force that demonstrated
clearly the power of the liquid hydrogen bubble chamber plus its associated
dataanalysis techniques.
Although only one 2° was observed in the short time the 15 in. chamber
was in the separated K beam, large numbers of events showing strange
particle production were available for study. The Franckcnsteins were kept
busy around the clock measuring these events, and those of us who had
helped to build and maintain the beam now concentrated our attention on
the analysis of these reactions. The most copious of the simple « topologies »
was K"p *■ two charged prongs plus a neutral Vpartielc. According to the
Recent developments in particle physics 35
strangeness rules, this topology could represent either
K"+p^A+7r++7r
I
71 +p
or
K~> p > K°+p+^ 
71 \ll +
The kinematics program, KICK, was now available to distinguish between
these two reactions, and to eliminate those examples of the same topology in
which an unobserved 7i° was produced at the first vertex. SUMX had not yet
been written, so the labor of plotting histograms was assumed by the two very
able graduate students who has been associated with the K~ beam and its
exposure to the 15 in. chamber since its planning stages: Stanley Wojcicki
and Bill Graziano. They first concentrated their attention on the energies of
the charged pions from the production vertex in the first of the two reactions
listed above. Since there were three particles produced at the vertex — a
charged pion of each sign plus a A — one expected to find the energies of each
of the three particles distributed in a smooth and calculable way from a mini
mum value to a maximum value. The calculated curve is known in particle
physics at the « phasespace distribution ». The decay of a t meson into three
charged pions was a wellknown « threeparticle reaction » in which the
dictates of phase space were rather precisely followed.
But when Wojcicki and Graziano finished transcribing their data from
KICK printout into histograms, they found that phasespace distributions
were poor approximations to what they observed. Figure 14 shows the
distribution of energy of both positive and negative mesons, together with
the corresponding « Dalitz plot », which Richard Dalitz [56] had originated
to elucidate the « t6 puzzle », which had in turn led to Lee and Yang's parity
nonconservation hypothesis.
The peaked departure from a phasespace distribution had been observed
only once before in particle physics, where it had distinguished the reaction
p+p^ 7i + +d from the « threebody reaction » p+p» 7r + +p+n. (Although
no new particles were discovered in these reactions, they did contribute to our
knowledge of the spin of the pion [57]). But such a peaking had been observed
in the earliest days of experimentation in the artificial disintegration of nuclei,
and its explanation was known from that time. Oliphant and Rutherford [58]
observed the reaction p+ n B>3 4 He. This is a threebody reaction, and the
energies of the a particles had a phasespacelike distribution except for the
fact that there was a sharp spike in the energy distribution at the highest
36
L. W. Alvarez
40 80 120 160 200 240 280 320 360400
TV+dVlev)
Fig. 14.  Discovery of the Y*(1385) (see text for explanation).
aparticle energy. This was quickly and properly attributed [58] to the reaction
p+ n B^ 8 Be+ 4 He
l He+ 4 He
In other words, some of the reaction proceeded via a twobody reaction,
in which one a particle recoiled with unique energy against a quasistable
8 Be nucleus. But the 8 Be nucleus was itself unstable, coming apart in 10~ 16 s
into two a particles of low relative energy. The proof of the fleeting existence
of 8 Be was the peak in the highenergy aparticle distribution, showing that
initially only two particles, 8 Be and 4 He, participated in the reaction.
The peaks seen in Fig. 14 were thus a proof that the Tii recoiled against
a combination of A+tt^ that had a unique mass, broadened by the effects of
the uncertainty principle. The mass of the Arc combination was easily calculable
Recent developments in particle physics
37
as 1382 MeV, and the /spin of the system was obviously 1, since the /spin
of the A is 0, and the /spin of the 7i is 1. This was then the discovery of the
first « strange resonance », the Yi(1385). Although the famous Fermi 3,3
resonance had been known for years, and although other resonances in the
nr nucleon system had since shown up in total crosssection experiments at
600 700 800 900
Mass of K IT system ( Mev )
Fig. 15.  Discovery of the K*(890).
38
L. W. Alvarez
Brookhaven and Berkeley, CalTech and Cornell [59] the impact of the Y*
resonance on the thinking of particle physicists was quite different — the Y£
really acted like a new particle, and not simply as a resonance in a cross
section.
25
20
15
"I 1 r
* +
96events
10
5
<i
Typical mass
uncertainty
I25events
96 events
1400 1500
M°(Mev)
1600
Fig. 16.  Discovery of the Y*(1405).
We announced the Yj at the 1960 Rochester High Energy Physics Con
ference [60], and the hunt for more shortlived particles began in earnest. The
same team from our bubble chamber group that had found the Yi(1385)
Recent developments in particle physics
39
now found two other strange resonances before the end of 1960 — the
K*(890) [61], and the Y£(1405) [62].
Although the authors of these three papers have for years been referred to
as « Alston et al. », I think that on this occasion it is proper that the full list
be named explicitly. In addition to Margaret Alston (now Margaret Garnjost)
and Luis W. Alvarez, and still in alphabetical order, the authors are : Philippe
Eberhard, Myron L. Good, William Graziano, Harold K. Ticho, and Stanley
G. Wojcicki.
Figures 15 and 16 show the histograms from the papers announcing these
two new particles; the K* was the first example of a « boson resonance »
found by any technique. Instead of plotting these histograms against the
energy of one particle, we introduced the now universally accepted technique
of plotting them against the effective mass of the composite system: S+tt for
the Yo(1405) and K+tt for the K*(890). Figure 17 shows the present state
of the art relative to the K*(890) ; there is essentially no phasespace background
in this histogram, and the width of the resonance is clearly measurable to
give the lifetime of the resonant state via the uncertainty principle.
700 800_ 900 1000 1100 1200
Mass of kV system (MeV)
Fig. 17.  Present day K*(890).
These three earliest examples of strangeparticle resonances all had lifetimes
of the oder of 10~ 23 s, so the particle all decayed before they could traverse
more than a few nuclear radii. No one had foreseen that the bubble chamber
could be used to investigate particles with such short lives; our chambers
40
L. W. Alvarez
had been designed to investigate the strange particles with lifetimes of lO 10 s—
lO 13 times as long.
In the summer of 1959, the 72 in. chamber was used in its first planned
physics experiment. Lynn Stevenson and Philippe Eberhard designed and
constructed a separated beam of about l.6GeV/c autiprotons, and a quick
scan of the pictures showed the now famous first example of antilambda
production, via the reaction
PH P
■A +
A
Fig, 18.  First production of antilambda.
Recent developments in particle physics 41
Figure 18 shows this photograph, with the antiproton from the antilambda
decay annihilating in a fourpion event. I believe that everyone who attended
the 1959 High Energy Physics Conference in Kiev will remember the showing
of this photograph — the first interesting event from the newly operating 72 in.
chamber.
Hofstadter's classic experiments on the scattering of high energy electrons
by protons and neutrons [63] showed for the first time how the electric charge
was distributed throughout the nucleons. The theoretical interpretation of the
experimental results [64] required the existence of two new particles, the
vector mesons now known as the co and the p. The adjective « vector » simply
means that these two mesons have one unit of spin, rather than zero, as the
ordinary tz and K mesons have. The co was postulated to have /spin = 0.
and the p to have /spin = 1 ; the co would therefore exist only in the neu
tral state, while the p would occur in the +, — , and charged states.
Many experimentalists, using a number of techniques, set out to find these
important particles, whose masses were only roughly predicted. The first
success came to Bogdan Maglic, a visitor to our group, who analysed film from
the 72 in. chamber's antiproton exposure. He made the important decision
to concentrate his attention on protonantiproton annihilations into five
pions — two negative, two positive, and one neutral. KICK gave him a selected
sample of such events; the tracks of the 7i° could not be seen, of course,
but the constraints of the conservation laws permitted its energy and direction
to be computed. Maglic then plotted a histogram of the effective mass of
all neutral threepion combinations. There were four such neutral combinations
for each event; the neutral pion was taken each time together with all four
possible pairs of oppositely charged pions. SUMX was just beginning to
work, and still had bugs in it, so the preparation of the histogram was a
very tedious and timeconsuming chore, but as it slowly emerged, Maglic
had the thrill of seing a bump appear in the side of his phasespace distri
bution. Figure 19 shows the peak that signaled the discovery of the very
important co meson.
Although Bogdan Magli6 originated the plan for this search, and pushed
through the measurements by himself, he graciously insisted that the paper
announcing his discovery [65] should be coauthored by three of us who
had developed the chamber, the beam, and the analysis program that made
it possible.
The p meson is the only one from this exciting period in the development
of particle physics whose discovery cannot be assigned uniquely. In our
group, the two Frankensteins were being used full time on problems that the
senior members felt had higher priority. But a team of junior physicists and
graduate students, Anderson et al. [66], found that they could make accurate
42
L. W. Alvarez
2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 I.I 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2
Q.
E
3
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 I.I 1.2 1.3 1.4 1.5 1.6 1.7 1.8 IJ9 2.0 2.1 2.2
Effective mass , M 3 (Bev)
Fig. 19.  Discovery of the <o meson.
Recent developments in particle physics
43
enough measurements direcly on the scanning tables to accompliesh a « Chew
Low extrapolation ». Chew and Low had described a rather complicated
procedure to look for the predicted dipion resonance now known as the p
meson. Figure 20 shows the results of this work, which convinced me that
the p existed and had its predicted spin of 1 . The mass of the p was given
as about 650 MeV, rather than its now accepted value of 765 MeV. (This
low value is now explained in terms of the extreme width of the p resonance.)
The evidence for the p seemed to me even more convincing than the early
evidence Fermi and his coworkers produced in favor of the famous 3, 3
pionnucleon resonance.
Fit
. 400
E
Is 300
« 200
100
( Constroinf)
♦
Lin. Quad. Quod. Quod. Lin. Lin. Lin. Lin.
X' : Prob(%) 50 4 50 75 93 90 50 65
Lin. Lin.
0.8% 35%
No. of events: 74 127 176 170 197 178 173 105
( 2J + I) 47T*. for J=l
■4 151 Quod . 22 25 28
CU 2 (m7r 2 )
Fig. 20.  First evidence for the p meson.
But one of the unwritten laws of physics is that one really has not made a
discovery until he has convinced his peers that he has done so. We had just
persuaded high energy physicists that the way to find new particles was to
look for bumps on effectivemass histograms, and some of them were therefore
unimpressed by the ChewLow demonstration of the p. Fortunately, Walker
and his collaborators [67] at Wisconsin soon produced an effectivemass
ideogram with a convincing bump at 765 MeV, and they are therefore most
often listed as the disco veres of the p.
Ernest Lawrence very early established the tradition that his laboratory
would share its resources with others outside its walls. He supplied short
lived radioactive materials to scientists in all departments at Berkeley, and
44 L. W. Alvarez
he sent longerlived samples to laboratories throughout the world. The first
artificially created element, technetium, was found by Perrier and Segre [68],
who did their work in Palermo, Sicily. They analysed the racioactivity in a
molybdenum deflector strip from the Berkeley 28 in. cyclotron that had been
bombarded for many months by 6 MeV deuterons.
We followed Ernest Lawrence's example, and thus participated vicariously
in a number of important discoveries of new particles. The first was the v\
found at Johns Hopkins, by a group headed by Aihud Pevsner [69]. They
analysed film from the 72 in. chamber, and found the yj with a mass of
550 MeV, decaying into 7t+tc~7i . Within a few weeks of the discovery of
the •/), Rosenfeld and his coworkers [70] at Berkeley, who had independently
observed the yj, showed quite unexpectedly that /spin was not conserved in
its decay. Figure 21 shows the present state of the art with respect to the o>
and 7) mesons; the strengths of their signatures in this single histogram is
in marked contrast to their first appearance in 72 in. bubble chamber experi
ments.
In the short interval of time between the first and second publications on
the y], the discovery of the Yq(1520) was announced by FerroLuzzi, Tripp,
and Watson [71], using a new and elegant method. Bob Tripp has continued
to be a leader in the application of powerful methods of analysis to the study
of the new particles.
The discovery of the S*(1530) hyperon was accomplished in Los Angeles
by Ticho and his associates [72], using 72 in. bubble chamber film. Harold
Ticho had spent most of his time in Berkeley for several years, working tirelessly
on every phase of our work, and many of his colleagues had helped prepare
the highenergy separated K~ beam for what came to be known as the K72
experiment. The UCLA group analysed the two highestmomentum K~
exposures in the 72 in. chamber, and found the E*(1530) just in time to report
it at the 1962 High Energy Physics Conference in Geneva. (Confirming
evidence for this resonance soon came from Brookhaven [73]).
Murray GellMann had recently enunciated his important ideas concern
ing the « Eightfold Way » [74], but his paper had not generated the interest
it deserved. It was soon learned that Ne'eman had published the same sug
gestions, independently [75].
The announcement of the S*(1530) fitted exactly with their predictions
of the mass and other properties of that particle. One of their suggestions was
that four /spin multiplets, all with the same spin and parity, would exist in
a « decuplet » with a mass spectrum of « lines » showing an equal spacing.
They put the Fermi 3, 3 resonance as the lowest mass member, at 1238 MeV.
The second member was the Yi(1385), so the third member should have a
mass of (1385) + (1385— 1238) = 1532. The strangeness and the multiplicity
Recent developments in particle physics
45
1000
800
600
>
0)
400
m
V.
200
c
>
o
600
jQ
E
IS
400
200
(a)
I.I  1.8 BeV/c
.5 BeV/c
ft
400
600
800
+ __ o
M (7r + 7r"7r )
MeV
000
Fig. 21.  Present day histogram showing w and v\ mesons.
of each member of the spectrum was predicted to drop 1 unit per member,
so the E*(1530) fitted their predictions completely. It was then a matter of
simple arithmetic to set the mass, the strangeness, and the charge of the
46 L. W. Alvarez
final member — the Q~. The realization that there was now a workable theory
in particle physics was probably the high point of the 1962 International
Conference on High Energy Physics.
Since the second and third members of the series — the ones that permitted
the prediction of the properties of the D~ to be made — had come out of our
bubble chamber, it was a matter of great disappointment to us that the
Bevatron energy was insufficient to permit us to look for the Q,~. Its widely
acclaimed discovery [76] had to wait almost two years, until the 80 in. chamber
at Brookhaven came into operation.
Since the name of the Q. had been picked to indicate that it was the last
of the particles, the mention of its discovery is a logical point at which to
conclude this lecture. I will do so, but not because the discovery of the Q.
signaled the end of what is sometimes called the population explosion in
particle physics — the latest list [77] contains between 70 and 100 particle
multiplets, depending upon the degree of certainty one demands before
« certification ». My reason for stopping at this point is simply that I have
discussed most of the particles found by 1962 — the ones that were used by
GellMann and Ne'eman to formulate their SU 3 theories — and things became
much too involved after that time. So many groups were then in the « bump
hunting business » that most discoveries of new resonances were made simul
taneously in two or more laboratories.
I am sorry that I have neither the time nor the ability to tell you of the
great beauty and the power that has been brought to particle physics by
our theoretical friends. But I hope that before long, you will hear it directly
from them.
In conclusion, I would like to apologize to those of my colleagues and my
friends in other laboratories, whose important work could not be mentioned
because of time limitations. By making my published lecture longer than the
oral presentantion, I have reduced the number of apologies that are necessary,
but unfortunately I could not completely eliminate such debts.
REFERENCES
[1] J. Chadwick: Proc. Roy. Soc. {London), 136 A, 692 (1932).
[2] C. D. Anderson: Science, 76, 238 (1932).
[3] M. Conversi, E. Pancini and O. Piccioni: Phys. Rev., 71, 209 (1947).
[4] S. H. Neddermeyer and C. D. Anderson: Phys. Rev., 51, 884 (1937).
[5] J. C. Street and E. C. Stevenson: Phys. Rev., 51, 1005 (1937).
[6] H. Yukawa: Proc. Phys.Math. Soc. Japan, 17, 48 (1935).
[7] C. M. G. Lattes, H. Muirhead, G. P. S. Occhialini and C. F. Powell: Nature,
159, 694 (1947).
Recent developments in particle physics 47
[8] E. Gardner and C. M. G. Lattes: Science, 107, 270 (1948).
[9] R. Bjorklund, W. E. Crandaix, B. J. Moyer and H. F. York: Phys. Rev., 77
213 (1950).
[10] J. Steinberger, W. K. H. Panofsky and J. Steller: Phys. Rev., 78, 802 (1950).
[11] A. G. Carlson (now A. G. Ekspong), J. E. Hopper and D. T. King: Phil. Mag.,
41, 701 (1950).
[12] H. L. Anderson, E. Fermi, E. A. Long, R. Martin and D. E. Nagle: Phys. Rev.,
85, 934 (1952).
[13] B. Cassen and E. U. Condon: Phys. Rev., 50, 846 (1936).
[14] K. A. Brueckner: Phys. Rev., 86, 106 (1952).
[15] W. Pauli and S. M. Dancoff: Phys. Rev., 62, 85 (1942).
[16] A. Pais: Phys. Rev., 86, 663 (1952).
[17] W. B. Fowler, R. P. Shutt, A. M. Thorndike and W. L. Whittemore: Phys. Rev.,
91, 1287 (1953); 93, 861 (1954); 98, 121 (1955).
[18] O. Chamberlain, E. Segre, C. Wiegand and T. Ypsilantis: Phys. Rev., 100, 947
(1955).
[19] G. D. Rochester and C. C. Butler: Nature, 160, 855 (1947).
[20] A. J. Seriff, R. B. Leighton, C. Hsiao, E. D. Cowan and C. D. Anderson: Phys.
Rev., 78, 290 (1950).
[21] R. Armenteros, K. H. Barker, C. C. Butler, A. Cachon and C. M. York: Phil.
Mag., 43, 597 (1952).
[22] L. LeprinceRinguet and M. L'Heritier: Compt. Rend., 219, 618 (1944).
[23] H. A. Bethe: Phys. Rev., 70, 821 (1946).
[24] R. M. Brown, U. Camerini, P. H. Fowler, H. Muirhead, C. F. Powell and
D. M. Ritson: Nature, 163, 47 (1949).
[25] C. O'Ceallaigh: Phil. Mag., 42, 1032 (1951).
[26] M. G. K. Menon and C. O'Ceallaigh: Proc. Roy. Soc. (London), A 221, 292(1954).
[27] R. W. Thompson, A. V. Buskirk, L. R. Etter, C. J. Karzmark and R. H. Rediker:
Phys. Rev., 90, 329 (1953).
[28] A. Bonetti, R. Levi Setti, M. Panetti and G. Tomasini: Nuovo Cimento, 10, 345
(1953).
[29] R. Marshak and H. Bethe: Phys. Rev., 72, 506 (1947).
[30] M. GellMann: Phys. Rev., 92, 833 (1953).
[31] K. Nishijima: Progr. Theor. Phys. (Kyoto), 12, 107 (1954).
[32] L. W. Alvarez and S. Goldhaber: Nuovo Cimento, 2, 344 (1955).
[33] T. D. Lee: Les Prix Nobel en 1957.
[34] C. N. Yang: Les Prix Nobel en 1957.
[35] L. W. Alvarez, F. S. Crawford, Jr., M. L. Good and M. L. Stevenson: Phys.
Rev., 101, 303 (1956).
[36] V. Fitch and R. Motley: Phys. Rev., 101, 496 (1956).
[37] S. von Friesen: Ark. Fys., 8, 309 (1954); 10, 460 (1956).
[38] R. W. Birge, D. H. Perkins, J. R. Peterson, D. H. Stork and M. N. Whitehead:
Nuovo Cimento, 4, 834 (1956).
[39] D. Glaser: Les Prix Nobel en 1960.
[40] R. H. Hildebrand and D. E. Nagle: Phys. Rev., 92, 517 (1953).
[41] J. G. Wood: Phys. Rev., 94, 731 (1954).
[42] D. P. Parmentier and A. J. Schwemin: Rev. Sci. Instr., 26, 958 (1955).
[43] D. C. Gates, R. W. Kenney and W. P. Swanson: Phys. Rev., 125, 1310 (1962).
[44] L. W. Alvarez, F. S. Crawford, Jr., and M. L. Stevenson: Phys. Rev., 112, 1267
(1958).
48 L. W. Alvarez
[45] L. W. Alvarez, P. Davey, R. Hulsizer, J. Snyder, A. J. Schwemin and R. Zane:
URCL10109, 1962 (unpublished); P. G. Davey, R. I. Hulsizer, W. E. Humphrey
J. H. Munson, R. R. Ross and A. J. Schwemin: Rev. Sci. Instr., 35, 1134 (1964).
[46] L. W. Alvarez, in Proc. Intern. Conf. Instr. HighEnergy Phys., Stanford, Califor
nia, 1966, p. 271.
[47] W. K. H. Panofsky, L. Aamodt and H. F. York: Phys. Rev., 78, 825 (1950).
[48] L. W. Alvarez, H. Bradner, P. FalkVairant, J. D. Gow, A. H. Rosenfeld,
F. T. Solmitz and R. D. Tripp: Nuovo Cimento, 5, 1026 (1957).
[49] L. W. Alvarez, H. Bradner, F. S. Crawford, Jr., J. A. Crawford, P. FalkVai
rant, M. L. Good, J. D. Gow, A. H. Rosenfeld, F. T. Solmitz, M. L. Stevenson,
H. K. Ticho and R. D. Tripp: Phys. Rev., 105, 1127 (1957).
[50] F. C. Frank: Nature, 160, 525 (1947).
[51] Ya. B. Zel'dovitch: Dokl. Akad. Nauk SSSR, 95, 493 (1954).
[52] C. S. Wu, E. Ambler, R. W. Hayward, D. D. Hoppes and R. P. Hudson: Phys.
Rev., 105, 1413 (1957).
[53] T. D. Lee and C. N. Yang: Phys. Rev., 104, 254, 822 (1956).
[54] F. S. Crawford, Jr., M. Cresti, M. L. Good, K. Gottstein, E. M. Lyman, F. T.
Solmitz, M. L. Stevenson and H. K. Ticho: Phys. Rev., 108, 1102 (1957).
[55] P. Eberhard, M. L. Good and H. Ticho: UCRL8878, Aug. 1959 (unpublished);
J. J. Murray: UCRL3492, May 1957 (unpublished); J. J. Murray: UCRL 9506,
Sept. 1960 (unpublished).
[56] R. H. Dalitz: Phil. Mag., 44, 1068 (1953).
[57] W. F. Cartwright, C. Richman, M. N. Whitehead and H. A. Wilcox: Phys. Rev.,
78, 823 (1950); D. L. Clark, A. Roberts and R. Wilson: Phys. Rev., 83, 649 (1951);
R. Durbin, H. Loar and J. Steinberger: Phys. Rev., 83, 646 (1951).
[58] M. E. L. Oliphant and E. Rutherford: Proc. Roy. Soc. {London), 141, 259 (1933);
M. E. L. Oliphant, A. E. Kempton and E. Rutherford: Proc. Roy. Soc. (London),
150, 241 (1935).
[59] R. L. Cool, L. Madansky and O. Piccioni: Phys. Rev., 93, 637 (1954); see also
references in R. F. Peierls: Phys. Rev., 118, 325 (1959).
[60] M. Alston, L. W. Alvarez, P. Eberhard, M. L. Good, W. Graziano, H. K. Ticho
and S. G. Wojcicki: Phys. Rev. Lett., 5, 520 (1960).
[61] M. H. Alston, L. W. Alvarez, P. Eberhard, M. L. Good, W. Graziano, H. K.
Ticho and S. G. Wojcicki: Phys. Rev. Lett., 6, 300 (1961).
[62] M. H. Alston, L. W. Alvarez, P. Eberhard, M. L. Good, W. Graziano, H. K. Ticho
and S. G. Wojcicki: Phys. Rev. Lett., 6, 698 (1961).
[63] R. Hofstadter: Rev. Mod. Phys., 28, 214 (1956).
[64] W. Holladay: Phys. Rev., 101, 1198 (1956); Y. Nambu: Phys. Rev., 106, 1366 (1957);
C. F. Chew: Phys. Rev. Lett., 4, 142 (1960); W. R. Frazer and J. R. Fulco: Phys.
Rev., 117, 1609 (1960); F. J. Bowcock, W. N. Cottingham and D. Lurie: Phys.
Rev. Lett., 5, 386 (1960).
[65] B. C. Maglic, L. W. Alvarez, A. H. Rosenfeld and M. L. Stevenson: Phys. Rev.
Lett., 7, 178 (1961).
[66] J. A. Anderson, V. X. Bang, P. G. Burke, D. D. Carmony and N. Schmitz: Phys.
Rev. Lett., 6, 365 (1961).
[67] A. R. Erwin, R. March, W. D. Walker and E. West: Phys. Rev. Lett., 6, 628 (1961).
[68] C. Perrier and E. Segre: Accad. Naz. Lincei, Rendi. Classe Sci. Fis. Mat. e Nat.,
25, 723 (1937).
Recent developments in particle physics 49
[69J A. Pevsner, R. Kraemer, M. Nussbaum, C. Richardson, P. Schlein, R. Strand,
T. Toohig, M. Block, A. Engler, R. Gessaroli and C. Meltzer: Phys. Rev. Lett.,
7, 421 (1961).
[70] P. L. Bastien, J. P. Berge, O. I. Dahl, M. FerroLuzzi, D. H. Miller, J. J. Mur
ray, A. H. Rosenfeld and M. B. Watson: Phys. Rev. Lett., 8, 114 (1962).
[71] M. FerroLuzzi, R. D. Tripp and M. B. Watson: Phys. Rev. Lett., 8, 28 (1962)
[72] G. M. Pjerrou, D. J. Prowse, P. Schlein, W. E. Slater, D. H. Stork and H. K.
Ticho: Phys. Rev. Lett., 9, 114 (1962).
[73] L. Bertanza, V. Brisson, P. L. Connolly, E. L. Hart, I. S. Mittra, G. C. Moneti,
R. R. Rau, N. P. Samios, I. O. Skillicorn, S. S. Yamamoto, M. Goldberg, L. Gray,
J. Leitner, S. Lichtman and J. Westgard: Phys. Rev. Lett., 9, 180 (1962).
[74] M. GellMann: Cal. Inst. Tech. Synchrotron Lab. Rep. CTSL20, 1961 (unpublished).
[75] Y. Ne'eman: NucJ. Phys., 26, 222 (1961).
[76] V. E. Barnes, P. L. Connolly, D. J. Crennell, B. B. Culwick, W. C. Delaney,
W. B. Fowler, P. E. Hagerty, E. L. Hart, N. Horwitz, P. V. C. Hough, J. E.
Jensen, J. K. Kopp, K. W. Lai, J. Leitner, J. L. Loyd, G. W. London, T. W. Mor
ris, Y. Oren, R. B. Palmer, A. G. Prodell, D. Radojicic, D. C. Rahm, C. R. Ri
chardson, N. P. Samios, J. R. Stanford, R. P. Shutt, J. R. Smith, D. L. Stone
hill, R. C. Strand, A. M. Thorndike, M. S. Webster, W. J. Willis and S. S. Yama
mqto: Phys. Rev. Lett., 12, 204 (1964).
[77] A. H. Rosenfeld, A. BarbaroGaltieri, W. J. Podolsky, L. R. Price, P. Soding,
C. G. Wohl, M. Roos and W. J. Willis: Rev. Mod. Phys., 39, 1 (1967).
Weak Interactions
and the Breaking of Hadron Symmetries.
N. Cabibbo
Istituto di Fisica delVUniversita  Roma
Istituto Nazionale di Fisica Nucleare  Sezione di Roma
L. Maiani
Laboratori di Fisica, Istituto Superiore di Sanitd  Roma
Istituto Nazionale di Fisica Nucleare, Sottosezione Sanitd  Roma
Introduction.
In a recent paper [1] we have proposed a dynamical relation among weak,
strong, and e.m. interactions, on the basis of a selfconsistency condition
which requires that the description of hadron physics remains unchanged
by the effect of leading weak corrections and e.m. tadpole effects. The main
results of this approach were a relation between the weak interaction angle 6
and the symmetry breaking parameters, and the appearance of a nonelectro
magnetic breaking of isotopic spin.
The presentation in ref. [1] was centered on the application of the self
consistency condition itself. This condition is, to a certain extent, arbitrary
at the present stage of the theory and a deeper understanding of the whole
subject is certainly needed to acquire more confidence in its validity. In this
paper we present a review of the whole theory putting a particular emphasis
on those aspects which do not require explicitly the use of the selfconsistency
condition. These aspects are interesting on their own, and pose many open
problems to future investigations.
In Sect. 1 we give an outline of hadron symmetries and their connection
to weak interactions. Section 2 contains a phenomenological analysis of
symmetry breaking. On this point we follow the analysis of GellMann
et al. [2] and of Glashow and Weinberg [3], and in addition we discuss the
necessity, at a phenomenological level, of introducing a nonelectromagnetic
isospin breaking. In Sect. 3 we discuss attempts to understand the structure
Weak interactions and the breaking of hadron symmetries 51
of symmetry breaking in terms of a purely strong interaction dynamics.
In this connection we give a simple derivation of a result due to Michel and
Radicati [4], indicating that the patterns of symmetry breaking preferred by
strong interaction bootstrap are those which reduce SU Z (x) SU 3 to either
SU 3 or SU 2 (x) SU 2 . Section 4 is devoted to an analysis of the consequences
of the none.m.isospin breaking previously introduced with respect to
y] > 3tc decay and to the mass splittings within isospin multiplets.
In Sect. 5 we study the possible strong effects of weak interactions. In
particular we show that if the explicit strong breaking of SU 3 (x) SU 3 trans
forms as a (3, 3) + (3, 3) representation, these corrections do not produce
a breaking of parity and strangeness at a strong level. We also show that
this is not true if the explicit breaking transforms as a (1, 8) + (8, 1).
Finally, in Sect. 6, we review our selfconsistency requirement and its
consequences.
1.  Investigations on symmetries in elementary particle physics have been
pursued with an ever increasing degree of effort and sophistication in the
last decade.
The wellestablished isospin symmetry acquired a new dimension with
the Conservation of Vector Current (CVC) hypothesis of Feynman and Gell
Mann [5], which identified the charged isospin currents with a part of the
vector current appearing in the weak coupling of leptons to hadrons. The
neutral currents related to I z and to the hypercharge Y were already identified
as components of the electromagnetic current. The CVC hypothesis thus
accomplished the program of giving a physical role to the generators of the
whole SU 2 ®U 1Y , which at that time represented (apart from baryonic number
and discrete symmetries) the full invariance group of strong interactions.
It was then natural to try the opposite approach, namely to give a sym
metry role to all currents with a physical meaning, and in particular to the
axial and the strangeness changing currents (both axial and vector) appear
ing in (3decays.
Consideration of the strangeness nonchanging axial current led to the
extension of the SU 2 group of isospin into the chiral SU 2 (x) SU 2 group. This
interpretation of the axial current has been made possible by the use of an
entirely new concept, i.e., that of a dynamically broken symmetry, introduced
by Nambu and JonaLasinio [6]. The chiral SU 2 (x) SU 2 symmetry, in fact,
is not realized in the usual way, as this would require all hadrons to appear
in degenerate parity doublets. Baryons not appearing in parity doublets
should have a vanishing mass, a possibility even further from physical reality.
That chiral SU 2 (x) SU 2 symmetry can nevertheless be realized is made plau
sible by the following argument: A continuous symmetry group implies
52 N. Cabibbo and L. Maiani
the existence of a set of operators commuting with the Hamiltonian. One
of these operators, when acting on a single particle state, should turn it into
states of the same mass.
In the usual realization of a symmetry, these new states are also one
particle states, and this requires particles to appear in degenerate multiplets,
which form a basis for a representation of the group in question. The gen
erators of a dynamically broken symmetry turn instead single particle into
multiparticle states, and in order for these states to have the same mass as
the original one, massless bosons must appear. In the case of chiral SU 2 (x)
(x) SU 2 , these bosons are identified with the pions, and the symmetry is exact
to the extent that one can neglect the pion mass. An axial generator turns
then, e.g., a single nucleon state into « one nucleon plus many pions » states
and this avoids the parity doubling of nucleon states. It is clear that the
hypothesis of chiral SU 2 ® SU 2 symmetry for strong interactions does not
lead to new predictions on hadron spectrum, but provides a powerful tool
for relating processes involving low energy (soft) pions. The exploitation of
soft pion theorems, pioneered by Nambu, has received a great amount of
attention in the last few years, yielding numerous results in good agreement
with experiments [7]. The same results have also been obtained by an equiv
alent approach based on the hypothesis of Partial Conservation of the
Axial Current (PCAC), introduced by GellMann and Levy [8].
Only after the discovery of SU 3 as an approximate symmetry of hadrons,
it has been possible to complete the program of giving a symmetry inter
pretation for the strangeness changing weak current. Since SU 3 is a symmetry
of the normal kind, akin to isotopic spin, it allows a classification of hadrons
in supermultiplets comprising multiplets of different isospin and strangeness.
The two extensions of SU 2 , i.e., chiral SU 2 ® SU 2 and SU 3 , both well
supported by experimental facts, can only coexist if they are subgroups of
a larger symmetry. The simplest possibility for the larger group is a chiral
SU 3 (x) SU 3 . Associated with this larger group is a set of eight vector and
eight pseudovector currents, Vj^x) and Afa) (i= 1,...,8). One can com
bine these currents into two sets:
0) JlVl + A^,
(2) Jp = V n A^ ,
whose charges generate two commuting SU 3 .
It has been conjectured [9] that the weak current of hadrons is a com
bination of these according to:
(3) J?* = cosd(J l __ ijt) + sin (/ 4 + /7 5) f
Weak interactions and the breaking of hadron symmetries 53
being a new, universal constant. Equation (3) has been used to give a
simple description of all [3decay processes, which has been fully confirmed
by the existing experimental data [10]. In particular has been determined
to be ~0.22.
The structure of the theory can be presented in a very simple way, using
the language of the quark model. In this model all hadrons are bound states
of the three quarks p, n, X, and their antiparticles. The quarks themselves
transform as the basic representation 3 of SU 2 . The symmetry currents /*
and J^ have the simple expression:
(4)
where li (7=1,..., 8) are the eight GellMann matrices. The hadronic
weak current, eq. (3), has the simple form:
(5) /; eak =py,(l + y 5 )[cos0w + sin0A] = fy^l + y s )X+y> ,
where
(0 cos0 sin0 N
In this picture the meaning of the parameter is particularly transparent.
The weak current has a specially simple form in terms of the three fields:
p, n' = cosdn + sinflA, A' = — sin0« + cos0A:
(7) Jjr k =PY l &+YJn'
Thus is seen to be the angle between the frame p, n, A and p, n', X' chosen
in the quark internal space by the SU 3 breaking and by the weak interactions
respectively. The current given by (5) and (7) displays exactly the same
structure as the (ev e ), (fxv^) pieces of the leptonic current, thus obeying the
requirement of universality of weak interactions. The universality principle
can be given a more abstract formulation in terms of current commutators [11],
and can be proven to be satisfied by eq. (3) without any reference to the
quark model.
su 2 ( 2 SU *® SU 3
^ su 2 ®su 2 s
Fig. 1.
54 N. Cabibbo and L. Maiani
2.  In the previous section we have outlined the emergence of a chain
of higher symmetries for hadrons, from SU 2 (x) U lY to SU s (x)SU 3 , according
to the pattern of Fig. 1 . We have also emphasized the deep connection between
weak and e.m. interactions on one side and the symmetry structure of strong
interactions on the other side. In this Section we will present a phenomeno
logical study of the breaking of these symmetries following the works of
refs. [2] and [3]. This discussion will be based on the usual assumption that
hadron physics can be described by a hierarchy of interactions, where the
main features of hadronic processes are determined by strong interactions,
with small e.m. and weak perturbation. This is in fact a very strong assumption,
which will probably be abandoned in the future developments of the theory.
As we shall see later, weak interactions can give rise to large effects, strictly
interwoven with what one would call proper strong effects.
With this proviso, let us write the hadron Lagrangian as:
(8) &=&M+&e J n.+ &*.
We shall also write j2? s = jS? + jSPj , where =^ is that part of the strong
Lagrangian which is symmetric under the full SU s (x) SU 3 group. We will
refer to <g x as the explicit breaking term of & s . In fact, even in the limit
=2\ = and neglecting weak and e.m. effects, one can still have a dynamical
breaking, as discussed in the previous section for the case of spontaneous
breaking of SU 2 (g) SU 2 . In this case a particular realization of =^ would
be characterized by a subgroup G of SU 3 (x) SU S , represented in the multi
plet structure of hadrons. To each of the SU 3 (g) SU 3 generators not belong
ing to G it would correspond a scalar or pseudoscalar massless boson. Some
possibilities are given in Table I. Only the first one appears to be near the
physical situation. In fact the hadron spectrum clearly exhibits the SU 3
multiplet structure, and the eight pseudoscalar mesons are the least massive
of known hadrons.
Table I.  Some possibilities for the spontaneous breaking of SU 3 xSU 3 . K s indicates a
scalar kappa meson.
Multiplet Structure Massless Bosons
SV» 7U, K, 7)
Chiral SU 2 ®SU 2 K, t], K s
SU 2 ® U 1T tz, K, ti, K s
A satisfactory description of ST/ 3 (x) SU 3 breaking appears then to be one
in which the symmetry of ^ is realized according to the first possibility of
Table I. The explicit breaking term jSf x would then cause a departure from
Weak interactions and the breaking of hadron symmetries
55
this situation, giving finite masses to the pseudoscalar mesons as well as mass
splittings within SU S multiplets. This picture provides a rational basis to
the observation that the masses of the pseudoscalar mesons are of the same
order of magnitude as their mass splittings, and of mass splittings within
other multiplets.
The fact that the pion mass is an extremely small quantity on the hadron
scale (m£ ^ 0.019 GeV 2 ) together with the considerations of Sect. 1 indicate
that the structure of J^ is such as to give a relatively large breaking of
SU s (g) SU 3 into SU 2 (x) SU 2 , and a much smaller breaking of chiral SU 2 (x)
(x) SU 2 . The success of the GellMannOkubo mass formula moreover
indicates that S£ x is a superposition of SU S singlets and octets. All these
requirements are met if we assume that £P X transforms as a component of a
(3, 3) ©(3, 3) representation of chiral SU Z ® SU 3 .
The basis for such a representation is a set of nine scalar and nine pseudo
scalar densities a* and n 1 [12], obeying the equaltime commutation relations:
[Vi,aj] =
[Vi,7lj] =
[Ai,7Tj] =
ifijkGk ,
ifijk^k ,
idtjicTik ,
— idijkGk •
In terms of these objects, (assuming parity and strangeness conservation)
SPl has the simple form:
(9) Se x = e Q a + £ 8 cr 8 + e z a z .
This picture has a simple transcription in quark language, where:
and the breaking term £P X can be interpreted as a quark mass term:
(10)
where :
(11)
&\ — X PP + finn + yAA
oc = l/3 £ o+^ + £3 '
fi«
P= V ***+!**•
V3
1h
7= ^ £ »Vf £8
56 N. Cabibbo and L. Maiani
The requirement that & x leads to a nearly exact SU 2 (x) SU 2 symmetry can
be stated as saying that p and n masses must be much smaller than the X
mass, i.e.
or, equivalently,
e 8 ?w — V2 e .
Detailed phenomenological analyses have been carried out in refsJ[2]
and [3], and indicate that:
(12) e 8 / £o ^1.25.
In eq. (9) we have attributed to j2\ also a term proportional to a z which causes
a breakdown of isospin symmetry, independent from the isospin breaking
induced by the electromagnetic interaction J? e . m .. The necessity of such a
term is indicated by two different theoretical results. The first one is a theorem
due to Bell and Sutherland [13], according to which in the soft pion limit
the isospin violating decay 7] > 3tc cannot proceed through e.m. interaction.
Bell and Sutherland have also shown that the observed decay rate is by at
least two orders of magnitude larger than what could be obtained introducing
the corrections for a finite pion mass. The second argument relies on a theorem
by R. Dashen [14], which states that, if isospin breaking is of a purely e.m.
origin the sum rule:
2 k + — m K!
mt+ — rrivo = ml+ — mi»
should be verified up to terms of order e 2 e 8 and e 2 e . The failure of this sum
rule, which reads:
— 4000 MeV 2 = 1260 MeV 2
has to be compared with the good agreement of the Coleman and Glashow [15]
sum rule:
E~—E = p — n+ E~—S +
which is derived also neglecting terms of order e 2 e 8 . The problems arised
by the theorems of Bell and Sutherland and of Dashen can both be solved
by introducing a <r 3 term in J^ . Question arises whether one can fix the para
meter e 3 in such a way as to obtain a quantitative agreement in both cases.
This question will be discussed in Sect. 4 where we will also analyze other
possible consequences of the <r 3 interaction.
Weak interactions and the breaking of hadron symmetries 57
3.  We want now to consider the question whether the structure of
symmetry breaking which we have studied at a phenomenological level, and
in particular the values for the parameters e , e 8 , e 3 , can be understood in the
framework of current theories of strong interactions.
Our present understanding of strong interaction dynamics is based
on the idea of bootstrap according to which the parameters of the theory
should be determined by selfconsistency conditions. The study of SU 3
breaking within a bootstrap theory has been pioneered by R. Cutkosky [16],
who found that solutions of the bootstrap are favored, where the breaking
reduces SU 3 to exact SU 2 . Michel and Radicati [17] have produced an
interesting geometrical insight into this result, and have recently ex
tended [4] their study to the breaking of SU 3 (g) SU 3 . We shall state here
their result, and discuss its limitations and its implications for our program.
In Appendix I we shall give a simple derivation of the MichelRadicati
theorem.
Let us assume that the bootstrap condition can be expressed as a varia
tional principle:
(13) 8G(e 3 ,e 8 ,e ) = 0.
Equation (13) will have to be completed by some other requirement, to be
called the « stability condition » which will select a solution of eq. (13) as
the physically relevant one.
We do not need to give here a specific form to these stability conditions;
they could simply consist in the requirement that the stable solution be a
minimum of G, or could be of a more complicated nature [18].
The result of Michel and Radicati then states that there exist always
solutions of eq. (13) which correspond to:
i) exact SU 3 (x) SU 3 (e 3 = e 8 = s — 0) ;
ii) exact SU 3 (e 3 = e 8 = ; £ ^ 0) ;
iii) exact chiral SU 2 ® SU 2 (e 3 =0; £ 8 = — V^ e o)
The significance of this result is limited by the consideration that one is
not able to prove the nonexistence of other solutions which might be more
« stable » than the previous ones.
The MichelRadicati theorem can be taken as an indication that strong
interactions favor solutions of the kind i), ii), iii), which are different from
the one observed (even if only slightly in the case of solution iii)). We obtain
therefore from their result some support to the idea that weak and e.m.
interactions play a nonnegligible role in determining the structure of the
breaking. In order to prove the existence of solutions ii) and iii), Michel
58 N. Cabibbo and L. Maiani
and Radicati restrict the range of variation of the e's to the unit sphere:
e 3 ~f~ £ 8 ~~t~ £ == 1 •
As shown in Appendix I this restriction can be justified by the physical
ipothesis that bootstrap equations are not able to fix the scale of hadron
masses, i.e., that G has the scale invariance property:
G{Ae z , Ae 8 , As ) = G(e 3 , e 8 , e ) .
4.  None.m. breaking of /spin.
In this section we describe possible physical consequence of a none.m.
breaking of isospin, as embodied in the term e s a 3 of J§f x .
Electromagnetism itself can give rise to corrections which imitate the
effect of such a term. These corrections are the socalled tadpole contributions
of the e.m. interactions. They arise from graphs of the kind shown in Fig. 2,
 cr? i "* i^o
Fig. 2.
which correspond to the annihilation into the vacuum of scalar mesons
associated with the a 3 , a 6 , and ff densities. We may separate this contribu
tions from J^e.m., by adding to the Lagrangian a counter term ^ c  m SC 1 , i.e.,
writing eq. (8) as:
(14) Js = ir f Jr 1 f =^ e.m. \ *^weak =
= =^o i <>&i~t~ o ' • J ^ 1 4" V^e.m. o ' ' ^i) ~r =^weak •
Therefore 8 e  m ^ ? 1 is determined by the following condition on the matrix
element for the transition of one scalar meson into the vacuum extrapolated
to zero fourmomentum:
(15) lim <0(^ e .m.  S"**^, P> = .
Weak interactions and the breaking of hadron symmetries 59
In the following we will indicate by £30^ the whole isospin breaking term of
S£ x \ S^J^, calling %e z a z it purely e.m. part:
(16) £ 3 #3 = ^(1— Z)<?3 + Z £ 3^3
Any isospin violating amplitude can thus the splitted into two terms, i.e. :
(17) (contribution of =2^ + ^ em ^ , 1 ) ++ (nontadpole e.m. contributions) .
The nontadpole contributions correspond to graphs different from Fig. 2,
e.g., of the kind shown in Fig. 3.
■&y///ys?)
Fig. 3.
We will first discuss the two cases, where, due to the theorems of Bell
and Sutherland [13], and of Dashen [14], the none.m. contribution to iso
spin breaking can be uniquely identified.
These two effects are the violation of the Dashen sum rule for K + —K°,
n + — n° mass difference, and the 7]^37r decay. In these cases it is conve
nient to decompose as in eq. (16) the isospin breaking Lagrangian, and use
the computational scheme:
(18) (isospin breaking effect) = (contribution of e 3 (l — %)a^) +
+ (total e.m. corrections) .
To lowest order in jSf l9 and neglecting e.m. effects, the masses of pseudo
scalar mesons are:
** H^ + ^ + ^l
60 N. Cabibbo and L. Maiani
+ *6l/ih
where particle symbols stand for the corresponding mass squared, C is the
reduced matrix element <jr(r7r>, and 8M* n is the yjtc mixing matrix element
induced by a z . The Dashen sum rule implies that the combination
(K + — K°) — (ti + — 7i°) = — 5260 (MeV) 2
is not affected, up to terms of order e 2 SC U by the e.m. corrections. This
allows a unique determination of the ratio e 3 (l— #)/e 8 according to:
(19) ^ri = _ (^^(^^ =
V3£s 2(K— 7r)
Using eq. (18) and the BellSutherland results one concludes that the
7) » 3tt amplitude is given by
(20) r=<37c ea (lz)*8h>.
We note at this point that models of yj decay based on the a z interaction had
already appeared in the literature. Only after Sutherland's result, however,
it became clear that such an interaction could not be a consequence of elec
tromagnetism.
Another class of models which have been advanced, is based on yju mixing,
and describes the decay as y\^k q ^3k or y] ^rpm ^7r°7i7r. Bell and Suth
erland have shown that such models cannot work if e.m. interactions only
are assumed. An insight into this result is given by the Dashen sum rule.
Using £/spin invariance one obtains:
(21) SM; n =l{(r^)(^^o)}
which, combined with the Dashen sum rule, shows that the mixing cannot
be ascribed to electromagnetism.
In Appendix II we give a simple derivation of the 73 > 3n amplitude
based on eq. (20). The result of this calculation is:
(22) r(yj > 3tt)
— y„ — „, 2
7T fc 8
Fie,
3f  £8 ^, Mjy u\ui y y
Weak interactions and the breaking of hadron symmetries 61
where F n = 2MxgA/gxxn & 1.21 M„ is the pion decay constant; S is the7r+Tc _
invariant mass, Q = M ri —3m v . and y = (T n o—T n <>)/T n <>. Equation (22) gives
a slope of the Dalitz plot distribution in excellent agreement with the experi
mental one. From the previous determination of e 3 (l — %)/e 8 , eq. (19), one
obtains :
(23) r(ti > 7r+7i7r ) sa 75 eV .
Using the experimental branching ratio for the yj > 7E + 7Tr7r° decay mode,
one can transform eq. (23) into a prediction for the total Yjwidth. One gets:
(24) r^ & 330 eV .
We do not try to attach an error to eq. (24). As an indication of the possible
range of variation of r , we may mention that a more refined determination
of our parameters e 3 , £ , e 8 , by G. Parisi and M. Testa [19], gives a values for
e 3 (l — x)/ s s as high as 1.6xl0 2 , which would lead to
(25) r„ & 600 eV .
Our prediction disagrees by a factor 3 f 6 from the value /^ =(2. 1 ±0.5) keV
established [20] on the basis of the measurement of the yj > yy width by the
Primakoff effect [21]. We note, however, that eq. (24) is in agreement with the
width obtained from 7i° lifetime and the use of SU 3 to relate the 7r°>2y
and yj » 2y rates [22]. A possible interpretation of the deviation of the
experimental yj > yy rate from the SU 3 value invokes the effect of yjX
mixing, with an abnormally large X°>yy coupling. We have not included
in our calculation the effect of yjX° mixing, but a rough order of magnitude
evaluation indicates that this effect should not change our prediction by
more than 10^30 % (which is the general order of magnitude of SU 3 breaking).
We cannot exclude that also in our case the discrepancy can be explained
by some abnormally large SU 3 breaking effect connected with yjX mixing.
A critical reconsideration of the experimental determination of yj ^ yy
might also be useful.
We consider now the problem of the isospin breaking mass differences
within the octet of stable, spin  baryons.
Using our previous consideration, and in particular eq. (19), we may
compute the effect of the nonelectromagnetic term e 3 (l— %)o 3 . We can then
split the experimentally observed mass differences into an electromagnetic
and a nonelectromagnetic part (see Table II).
A first qualitative conclusion one can draw from Table II, is that the
part ascribed to electromagnetism is either very small, or has the « natural »
62 N. Cabibbo and L. Maiani
Table II.
M exp (MeV)
«s(l — Z)^3
e.m.
£3 ff 3
nontadpole
pn
1.3
2.0
+ 0.7
1.6
+ 0.3
S"S°
4.9
+ 3.0
+ 1.9
2.4
+ 2.5
S°S+
3.1
+ 3.0
+ 0.1
2.4
+ 0.7
H E°
6.6
+ 4.0
+ 2.6
3.2
+ 3.4
sign, corresponding to charged particles heavier than neutrals. The analysis
of the baryon mass differences can also be carried out along the first of the
procedures indicated above, eq. (17). This corresponds to the wellknown
tadpole analysis of Coleman, Glashow and Socolow [23]. Their results appear
in the last two columns of Table II. Comparing the second and fourth columns,
one can obtain the value of (1— #), i.e. the ratio of the nonelectromagnetic
tadpole to the total tadpole contribution. The result is:
(26) 1*«1.2.
Again, we are not able to attach errors to this determination, which however
should not exceed rm 20%. The parameter %, which determines the strength
of the e.m. tadpole is then expected to be:
(27) Z^0.2.
It emerges from Table II that actually the none.m. terms provide the main
part of the isospin breaking mass differences. This suggests the possibility
that one can obtain rough estimates of other Al = 1 isospin breaking effects
by considering the contribution of this interaction.
As an example let us consider the problem of corrections to ttJV scattering
lengths.
We find that the charge independent relation:
(28) a(rp > 7r°n) = — = {a(n+p)  a(^"p)}
V z
after inclusion of the £ 3 (1 — %)a z term is modified into:
(29) a(7rp ► 7i0 n ) = i± (a(u+p)  a(np)} ,
V l
Weak interactions and the breaking of hadron symmetries 63
where:
(30) d = (M ° ^p)°one.m. ^ QJ x 1Q _ 2 _
This correction is about one order of magnitude smaller than the present
uncertainties on the measurements of the amplitudes involved, so that a
test of eq. (29) is at present impossible.
5.  We have anticipated in Sect. 3 that weak interactions may lead to correc
tions to hadron processes competitive with strong and e.m. effects. The
study of this poses a very complicated mathematical problem, which has
been solved up to now only in part and for expecially simple cases.
Let us assume weak interactions to be mediated by a vector boson coupled
to the SU z 0SU 3 hadron currents. The simplest model consistent with our
present understanding requires only one charged boson, coupled to the current
given in eq. (3).
The possibility of large corrections due to weak interactions is indicated
by the appearance of highly divergent integrals in the computation of these
effects with perturbation theory. If one introduces a regularization procedure
through a cutoff A y one finds at order 2« divergent terms of order (GA 2 ) n ,
where G is the Fermi constant, followed by less divergent terms of order
GiGA 2 )™' 1 , G(GA 2 ) n ~ x \ogA, etc.
A way to extract information from the perturbation theory under such
circumstances has been proposed by T. D. Lee [24]. It consists in resumming
the series according to the order of divergence, and then letting A > oo.
This procedure would lead to the following expression, for the regularized
^matrix :
(31) S = S^\GA 2 ) + GS^\GA 2 ) + ... ,
where S i0) (GA 2 ) contains all the terms of order (GA 2 ) n , i.e., the leading divergent
terms, S^iGA 2 ) contains the terms of order G(G'/l 2 ) w ~ 1 and so on. Going
to the limit A~>oo, if S i0) , S^\ etc. have finite limits, one would have ob
tained a new expansion of S in powers of G with finite coefficients. In par
ticular the first term S {0) (GA 2 ) gives the Smatrix a contribution completely
independent from the Fermi constant.
This program is complicated by the presence of logarithmic divergences,
which would probably require a separate treatment, and by the fact that
only the first term of eq. (31) is in general unambiguous. The subsequent
terms are expected to depend upon the way in which the theory is regularized.
We will restrict our analysis to the first term in eq. (31), which is expected
to contain all the possible « strong » effects due to weak interactions, and
64 N. Cabibbo and L. Maiani
leave open the important problem of the other terms, which are expected to
give the true, order G or higher, weak corrections.
Let us assume strong interactions to be described by a Lagrangian:
\j1) Jz s = Jzq \ ~z? i ,
where J? is invariant under SU 3 (x)SU 3 , and <£ x represents the symmetry
breaking. Hadronic weak interactions are assumed to be described by the
Lagrangian:
(32) ^weak = S(^+h.C.),
where /„ is the current eq. (3), and g is related to the Fermi constant by:
G = v / lg 2 M~ 2 . Let us define:
(33)
e+=Jd 3 x/ (x)
It is instructive to consider a second order calculation of weak corrections to
any strong amplitude A(oc > (5), where a and (5 are hadronic states. This is
given by:
(34) ^ = £J d .,_^(_,„ + 4*).
r exp [iqx] [<fi\T(Jp{x)J*(0))\K> + c.c] d*x .
■/•
Assuming the validity of Bjorken's limit, quadratically divergent terms arise
only from the q /i q v term, and are therefore connected with the nonconserva
tion of the weak current, i.e., to the symmetry breaking term =2^. Introducing
a cutoff A, by standard manipulations one finds the quadratically divergent
term to be [25]:
(35) 8< 2 U=/</ff8<2)js? 1  a >
with
GA 2
(36) S^ = 2"{[S + , lQ ~> ^ + [e "' [Q+ > ^D) '
From eq. (36) we see that §( 2) A is equivalent to the shift in A caused by
the addition of a piece S^jSfj. to J^, when S^J^ is treated perturbatively
to lowest order. If one goes to the fourth order weak corrections, one finds
Weak interactions and the breaking of hadron symmetries 65
a term which corresponds to the second order perturbation in 8^Sf lt as
well as other terms which should be identified with a further shift, 8( 4) J^ l5
of J?!, treated to lowest order.
This circumstance suggests that the leading weak corrections to any
strong process might be equivalent to a modification of S£ x \
(37) JS? 1 JJSf 1 + 8 weak JS?i,
where :
(38) 8 weak ^ = W>& x + S (4) ^i + ... .
In the general scheme of weak interactions we have described till now, this
is only a conjecture as yet unproven, and we have not even a complete analysis
of SWjgf 7 !. There are however models where this conjecture can be proven,
and the structure of S weak J^! written down in detail. Two models of this
kind were studied in ref. [1]. They are the free quarks model and models
allowing nontrivial strong interactions, but where weak interactions are trans
mitted by a neutral vector boson. The neutral boson is coupled to the cur
rent J^, defined by the relation:
(39) Q=jd*xJ (x) = i[Q + , QT}.
The second model was analyzed under the assumption that the breaking
term & x transforms as a (3, 3) © (3, 3) (which is necessarily the case for
quarks). In both cases it was found that, if £P X is characterized by a 3 x 3
matrix h (see Appendix I, eq. (1.1) and (1.3)), then & x + 8 weak ^ corresponds
to the matrix Ti:
(40) h = h + 8 weak /* = h — g {A+, X~) h ,
where X+ is the matrix defined in eq. (6), X~ its Hermitian conjugate, and 
is a real parameter. This result is the same that one would obtain at second
order, eq. (36), if one put £ = GA 2 . In the quark model g remains as a
parameter as yet undetermined, whereas in the neutral case £= 1.
An important feature of this result is the following. Suppose we start
from a parity and strangeness conserving ^ x , i.e. with a diagonal and real
matrix h. Equation (40) then implies that h is also a real matrix so that, by
Theorem 1 of Appendix I, h is equivalent to a real and diagonal matrix h D :
(41) h=Wh D V.
This means that the leading weak corrections do not cause a breaking of
parity and strangeness, which should only arise at order G. This however
66 N. Cabibbo and L. Maiani
is a peculiar property of the (3, 3) © (3, 3) behavior of the breaking S£ x .
In fact one can easily show that if ££ x contains a part which transforms as
(8,1)0(1,8), this result is not valid, and strong parity violations arise.
Proof of this is given in Appendix III, both using the second order calcula
tion, eq. (36), and the neutral vector boson model, treated to all orders.
We have emphasized in Sect. 1 the remarkable connection between weak
currents and strong interaction symmetries. The result we have just quoted
together with the indication discussed in Sect. 2 that symmetry breaking is
of a (3, 3) © (3, 3) kind, adds a new piece of evidence for the strict dynamical
intertwining of weak and strong interactions. Coming back to the case
when J£\ belongs to a (3, 3) © (3, 3) we note two facts.
First is that the transformation (41), which reinstates parity and strange
ness, changes the value of the weak interaction angle. We will call 6 the
uncorrected angle (i.e. the angle in the frame where h is diagonal) and 6 the
one in the frame of h D , i.e. the physically observed one. The angle appearing
in eq. (40) through X + and X", is obviously 6 , and 6 is a function of , h, and O ,
as discussed in Sect. 5 of ref. [1].
We finally note that even if h conserves isospin symmetry, h D will in
general not do so. Weak corrections thus seem to give a natural explanation
for the origin of the none.m. isospin breaking which is required by the
phenomenological analysis of Sects. 2 and 4, and which is not easily under
stood on the basis of strong interactions dynamics.
6.  We have studied till now the separate effects of e.m. and weak cor
rections on hadron dynamics. In this Section we will collect these different
results, and introduce a selfconsistency condition [1] which links at a dynam
ical level, the different interactions and allows a determination of the angle d
in terms of other parameters.
Starting from the equation:
(42) se = se* + sei + ^ e . m . + ^
and following the results of Sects. 3 and 5, we separate the leading weak
corrections and e.m. tadpole contributions according to:
(43) ££ = Cf Q + ^ + §weak ^ + §e.m. ^ +
+ (^e. m .— 8 e  m =^l) + (&— 8 Weak ^i) •
The last two terms correspond to nontadpole e.m. corrections and to non
leading, i.e. order G, weak corrections. As explained in ref. [1], Sect. 3,
ge.m.^ depends in a peculiar way on the explicit breaking.
Weak interactions and the breaking of hadron symmetries 61
If we define:
(44) 8 em  jSf x = I Tr (M + SA e  m  + $h e  m * M)
the result of ref. [1] is that S/* e  m  is diagonal in the same SU 3 (g)SU 3 frame
as the explicit breaking. The strength of SA e  m  is, on the other hand, mainly
determined by the dynamical breaking of SU 3 ® SU 3 . Since this, according
to the discussion of Sect. 2, reduces SU 3 (x) SU 3 into a nearly exact SU 3 ,
we expect 8/* e  m  to be a nearly exact £/spin singlet.
We have seen that the effect of weak corrections is to change the explicit
breaking from ^(/z) to & x (h D ). Then U e  m  will still be diagonal with h D
and will be changed only slightly by this modification, as it is expected to
depend mainly upon the dynamical breaking. The combined effect of weak
and tadpole e.m. interactions then changes the explicit breaking Lagrangian
^(h) appearing in eq. (42) into Sejfrv + 8/* e  m ).
The selfconsistency condition of ref. [1] requires h to be stable under
these effects, i.e.:
(45) h D + §/i e  m  = h .
Equation (45) gives a relation among the parameters a, /?, y, g, and either 6
or O . We will not report here the complete structure of eq. (45), but simply
give the results, valid in the case where /S/y < 1 and £j8/y < 1. One ob
tains the relations:
(46) «.^ W
(47) I
y Vil/2
a — jff a e.m._ j ge.m.
Equation (47) implies that only a portion I of the isospin breaking contained
in h D + 8/z e  m  is due to pure electromagnetism. The remaining fraction
(1_) i s nonelectromagnetic, so that £ has to be identified with the param
eter % introduced phenomenologically in Sect. 4. Substituting into eq. (46)
the result found there, eq. (27) and the value for 0/y deduced from eqs. (12),
(22) and (26), one finds a prediction for 6:
(48) 6 ** 0.25 .
7.  An outlook.
We have presented here a review of some recent developments in the
study of the dynamical interplay of weak, electromagnetic and strong in
teractions.
68 N. Cabibbo and L. Maiani
The best established consequence of this approach is the natural expla
nation for a new kind of isospin breaking, not uniquely electromagnetic.
This new term is required for the interpretation of experimental data con
cerning 7^decay and the mass differences of pseudoscalar mesons.
A second result which might suggest ideas of future development is the
realization of the special dynamical role of a symmetry breaking of the
(3, 3) © (3, 3) kind, which gives a fair description of experimental facts.
Among « simple » breaking schemes this is the only one which allows parity
to be conserved by the leading weak corrections.
Finally, the introduction of a new hypothesis, of a selfconsistency con
dition among weak, electromagnetic, and strong interactions gives a rela
tion between 6 and other phenomenological parameters which yields an
excellent prediction for 6.
Although these problems have been partly clarified, there remains a great
amount of work to be done on them, in particular in the treatment of higher
order corrections with a W ± boson. The model with a W boson, although
suggestive, is far from representing the real situation.
Other serious problems relating to higher order weak corrections have
not be touched. The most serious one is that of the selection rules observed
in weak decays (A5'<2, A/<, no neutral currents, etc.). Simple compu
tations at second order indicate a breakdown of each of these rules at order
G X GA 2 z& G. In order to agree with experiment, the theory should com
pensate this breakdown, perhaps at higher orders.
On the other hand the solution of the parity problem at the GA 2 level
leads some credibility to the hope that these harder problems will also be
solved.
Appendix I.
In this Appendix we give a simple algebraic proof of the MichelRadicati
result.
The possible dependence of G on e 3 , s 8 , s is restricted by symmetry con
siderations. To exploit them it is convenient to give a more general definition
of the symmetry breaking Lagrangian.
Starting with the densities at and m defined in Sect. 2, we define a
3x3 matrix M:
8
(1.1) M = 2>, + *rc<)A<,
where h are the usual GellMann matrices (A = V2/3). Under an element
Weak interactions and the breaking of hadron symmetries 69
(U, V) of SU 3 ®SU 3 , M transforms as:
(1.2) M>UMV i U, V= unitary, uninodular 3x3 matrices.
Since J^ is an element of this (3, 3) © (3, 3) representation of SU 3 ® SU 3
it can be identified by a 3x3 matrix h according to:
(1.3) J2\(A) = J Tr (A + M + M^h) .
Under a transformation (U, V), £P X transforms as:
(1.4) &&)>&&')
(1.5) h'=U*hV
Definition. Any pair of matrices h and h', obeying eq. (1.5) are called
equivalent: /z~/z'. In fact =2\(/z) and j£?i(A') have the same physical content,
because they are related by a change of basis under which ££ Q is invariant.
Theorem 1. If det/* is real, h^hj) where:
/a 0\
(1.6) h D = I /? 1 «>/?,/ being real numbers .
A proof of this theorem is given in ref. [1]. In this language, the bootstrap
condition which determines the breaking must have the form:
(1.7) $G(h) = .
Since two equivalent matrices have the same physical content, one must
have:
(1.8) G(h') = G(h) if h'~h.
Then G(h) is a function of the three SU 3 (x) SU 3 invariants one can con
struct out of h. These are:
(1.9) x 1 = T 2 (hh i ), x 2 = Tr [(M + ) 2 ] , x 3 = deth.
For diagonal matrices hp, we have:
(1.10) ^ = a 2 + i8 2 +y 2 ; jc 2 = a* + /S 4 + y* ; x 3 = ofty.
In the following we restrict our study to solutions which are parity conserving,
i.e. such that det/z is real.
70 N. Cabibbo and L. Maiani
Theorem 2. Up to an equivalence, all the parity conserving solutions to
eq. (1.7) are obtained as solutions of the equation:
(1. 1 1) %G(x x ((x, ft, y), x 2 (cc, ft, y), x 3 (oc, ft, y)) = ,
the variation being done in respect to a, fi, y, assumed to be real numbers.
This means that we can restrict in eq. (1.7) to real diagonal matrices h D , thus
recovering the variational principle given in Sect. 3.
Proof. For any h we have:
h = u*h D V
with suitable unitary, unimodular matrices U, V, and a diagonal h D . Moreover :
h + 8h = U'\h B + Bh D )V'
where U' and V are infinitesimally different from U and V and §h D is diagonal.
One then has, using eq. (1.8)
8G = G(h + 8/0— GQi) = G[U'\h D + M D )V']—G{U^h D V) =
= G{h D + %h D )G{h D ).
Although a, ft and y can vary through the whole 3dimensional space, x 1 ,
x 2 , x 3 are restricted to a definite domain D. The boundary of D is composed
by continuous surfaces, joined by edges which meet at singular points. The
equations for the different elements of the boundary can be obtained as follows :
Define vectors H = (oc,fi,y) and X = (x 1? x 2 , x 3 ). To a variation $H there
corresponds a variation
The elements of the boundary are characterized by special properties of d E X.
I'l. Characterization of surfaces.  Denote by n(x) the normal to the
surface pointing outwards from D. The variation 8 S X must be orthogonal
to n for any choice of 8H:
(1.13) nS H X=0.
Proof. For any $H, X must always remain in D, i.e. nS s X<0. Since
$ H X is linear in 8H, inequality can only be fulfilled as an equality.
1*2. Characterization of the edges.  Denoting by l(x) the unit vector
tangent to the edge, by the same argument as before one must have:
(1.14) $ B X parallel to /.
Weak interactions and the breaking of hadron symmetries 71
I'3. Characterization of singular points.  Arguing as before, one gets:
(1.15) S H X=0.
Conditions 1, 2, and 3 are equivalent to the requirements that the Jacobian
matrix :
/2a 2/3 ly
\Py yoc ocfi,
has a rank equal to two, one, and zero, respectively. One finds that, on the
boundary, one must have:
(1.17) detJ = 8(a 2 W 2 y 2 )(y 2 a 2 ) = 0.
This implies that on the boundary of D, two eigenvalues of h D are equal
(the solution, e.g., <x, — a, y is equivalent to the solution a, a, y). The sur
faces then correspond to SU^®U X . On the edges, the Jacobian matrix
should be of rank one. This implies either:
i) a 2 = /3 2 = y 2 , i.e. exact SU S . These equalities have two inequivalent
realization: (a, a, a) and (—a, —a, —a), corresponding to the two edges:
x a 1
(1.18) x 2 =^; x 3 =±xl;
r 2
J:
3 ' ~ 3 ^27
or
ii) a = ft = 0, y^O and permutations, i.e. exact ,SC/ 2 (x) »St/ 2 . Thus ii)
corresponds to a single edge, where one has:
(1.19) x 2 = x\; x 3 = 0.
There is only one singular point, where /= 0, i.e. the origin corresponding
to exact SU 3 (g) SU 3 . Solving eq. (1.17) for a, and substituting into eq. (1. 10),
one gets a parametric representation of the boundary. In Fig. 4 we report
a section x x = const of D. Points A, B, C are the intersection of the edges
with this plane. Points B and C correspond to eq. (1.18) and A to eq. (1.19).
The following theorems establish the conditions for the existence of extremal
points of G on the boundary of D:
Theorem 3. If X is a point on the surfaces composing the boundary
of D, and is an extremal point with respect to the values assumed by G on
this surface, then X is an extremal point for G in D.
Proof. The condition for X to be an extremal point of G in D is:
VG8 H *=0.
72
N. Cabibbo and L. Maiani
If X belongs to a boundary surface, § H Xis tangent to it, by eq. (1.13), and
the components of VG along the surface are zero by hypothesis.
0.2
0.1
o
Fig. 4.
0.1
*3
0.2
Analogously one can prove the following theorems:
Theorem 4. If A" is a point on an edge of D, and is an extremal point
with respect to the values assumed by G on this edge, then X is an extremal
point for G in D.
Theorem 5. If X is a singular point on the boundary of D, it is an ex
tremal point for G in D.
In spite of these theorems, we are still not in position to prove the
MichelRadicati result, apart from the existence of an extremal point cor
responding to the case of no breaking. The reason is that, since the boundary
of D has an infinite extension, there is no guarantee for the existence of an
extremal point on it. In order to conclude the proof of the theorem, a further
assumption is needed, which permits the search of an extremal point in a
region of finite extension.
We assume that the bootstrap conditions are not able to fix the scale of
the masses, i.e. the scale of a, /S, and y. This implies that G depends only
upon the ratios x 2 /x, x z \x\ and is therefore constant along the edges of the
boundary. Each point of this edge is therefore (by Theorem 4) an extremal
point of G on D. Moreover one can limit the search of extremal points of G
on the crosssection x 1 =\, analogous to that given in Fig. 2. If G is limited,
it will have at least one point of minimum and one of maximum on this
(finite) domain, which may or may not coincide with the extremal points A y
B and C.
Weak interactions and the breaking of hadron symmetries 73
Appendix II.
We give here a derivation of the t\ > 3iz amplitude given in Sect. 4
eq. (22), using the method of nonlinear realization of chiral symmetry given
by Coleman, et al. [26]. These authors have shown that the results of current
algebra and PCAC can be obtained by the use of phenomenological Lagran
gians in the tree graphs approximation. They have also given rules for writing
down these Lagrangians, and have shown the uniqueness of such a description.
The eight pseudoscalar mesons are represented in this formalism by a
3x3 traceless matrix:
(11.1) Jt=2V< (i=l,... ,8).
i
The SU 3 (x) SU 3 symmetric Lagrangian for amplitudes involving pseudoscalar
mesons only is:
(11.2) ^o^yTrOv^),
where p M is the covariant derivative of the pseudoscalar fields, defined in
ref. [26]. An expansion of p^ in powers of n is:
(II 3) p,, =  — dpTi — =  3 [[3^, n\ n\  ... .
The phenomenological form of the symmetry breaking ^ is:
(IL4) JSfi = e,(l  x) S 3 + e 8 S 8 + e S ,
where St are functions of jrfields which transform according to the (3, 3) ©(3, 3)
representation of SU 3 ® SU 3 . The choice of these functions is also unique,
and they can be obtained from the formal definition:
(115) S + iy 5 P = exp
A development of the righthand side of eq. (II. 5) in power series gives:
(116) S=l—= i 7i i + T = i ^
1 2 , J_
F 2 * + 3F*~
01.7) P=^7l~7l*+....
Thus jSft contains terms bilinear in the jzfields. The coefficients of these terms
give the mass matrix, including 7)7r° mixing. The elements of the mass matrix
74
N. Cabibbo and L. Maiani
agree with those given in eq. (18) of Sect. 4, provided one sets: C = 4F^ 2 .
We can diagonalize this matrix, the lowest order in e 3 (l — #)/e 8 introducing
two new fields fc and r\ which describe the physical r] Q and n Q fields:
(II.8)
71 = 71^ — fj s ,
V =r ls
2e 8
2e«
The amplitude for vj > tttt+tt  can then be calculated by the terms of J§? + jS^
quadrilinear in n. There are in principle three such contributions. Two of
them come, through the action of mixing, from if and from s s S 8 + s S .
Actually the second contribution vanishes in this case. The last contribution
comes directly from the term £ 3 (1 — x)^s The two nonvanishing contribu
tions are:
(II.9a)
(11.96)
2 %(!*)
3 n*
(3S—P 2 —q 2 — k 2 —p 2 )
3 e a F 2 K * n) '
~8*n
where P, q, k, p are the momenta of vj, tc+, tt , 7i, and s = (q + k) 2 = (P — p) 2 .
The total amplitude is then:
(11.10) T
2* 8 (1Z)
Kh
'■r^\{P*M$\{q* + k*+p*3m*^
which reduces on the mass shell to eq. (22) given in Sect. 4. From the well
known relation:
(11.11)
d»A)=i[Q\,^}
where Q\ are the axial charges, and through the definitions, eqs. (II.4) and (II. 5),
we see that the divergences of axial currents turn out to be proportional to
the Pis. This means in turn that PC AC is valid only up to terms trilinear
(or higher) in jrfields.
Even in presence of the £ 3 (1— %) breaking term, one can define suitable
combinations of A* and A*, whose divergences are proportional to the n
or rj fields, eq. (II. 8), up to terms of higher order in pseudoscalar fields. In fact
one has:
(11.12)
A*
A\
A* \ _L Al
C 3 A3
Weak interactions and the breaking of hadron symmetries 75
and
(11.13)
F m 2 „
F M %
This means that in processes involving less than three pseudoscalar mesons,
and in the three graphs approximation, the 7rfields can be treated as diver
gences of suitable currents. In particular they will satisfy the Adler consistency
condition, and moreover the effect of the S^breaking reduces in this case
to the effect of current mixing, eq. (11.12).
For processes with many pseudoscalar mesons the additional terms,
present in axial current divergences in this scheme, cause a failure of the Adler
consistency condition. Choosing a nonlinear realization different from the
« standard one » given in ref. [26], one could restore the Adler zero's for
pions. This however does not affect on the mass shell amplitudes since, as
shown in ref. [26], these amplitudes are independent from the particular
representation chosen.
We consider now nJf scattering in the soft pion limit. One can treat
this according to the method of Weinberg, using as interpolating fields the
axial divergences:
V^ a A ±
for iz+ and nr, and eq. (II.8) for ic°. One then easily finds that there is no
modification to the Weinberg formula for A(iz + p) — A(izp), whereas the
charge exchange amplitude is given at threshold by:
, TT1 „ . A + — A~ ( (MpM n )non.e.m. \
(11.14) ^^—.^l _ j,
where (M p — M n )none.m. indicates the none.m. protonneutron mass differ
ence, as given in Table II, of Sect. 4.
Appendix III.
In this Appendix we consider the leading weak corrections to hadron
processes in a fictitious model where nonleptonic weak interactions are ascribed
to the coupling of a neutral vector boson W only. We assume strong in
teractions to be described by the Lagrangian
(HI. 1) ^ s = ^ (v»<, 3„y *) + ^i(v') .
where ^ is invariant under SU 3 (g) SU 3 and J? lt the breaking term, is as
sumed not to contain derivatives. \p l represent a set of hadron fields, having
16 N. Cabibbo and L. Maiani
definite transformation properties under SU 3 (x) SU 3 . If we call F* the sixteen
generators of SU 3 (x) SU 3 , we have:
(III.2) [F°,y> i ] = iT? j y>1,
where the matrices T% constitute a representation of the generators F a .
Weak interactions with the neutral vector boson are assumed to arise
from the minimal substitution:
(ni.3) a^'^v' + fc^^,
where Tis the representative of the current to which Wis coupled. To connect
this model to the realistic one discussed in Sect. 5, where weak interactions
are mediated by charged vector bosons, we choose T to correspond to the
third component of weak isospin, i.e. T corresponds to the charge Q 3
defined as:
(H.4) Q s = m + ,Q~]
with Q ± defined as in eq. (33) of Sect. 5. In the quark language:
e 8 = V^A»(l+y 8 )v'
(HI 5)
a 3 =i[A + ,n
sin 2
6 is the weak interaction angle in the SU 3 ® SU 3 basis in which J^ is parity
and strangeness preserving. We also introduce minimal electromagnetic
coupling, and write:
(111.6) se = J2? (y', D^f) + ^(y»*) + J^ ph + ^ w ,
=^ph and i?w are the free photon and Wmeson Lagrangians, and we have
defined D^ip* to be:
(111.7) Drf = dptp* + igWJ i0 1 + ieA&yipt ,
Qtj being the matrix representing the electric charge.
To isolate the leading weak corrections, it is convenient to make use of
the Stuckelberg formalism [27], following the work of ref. [24]. This con
sists in decomposing W ^ into two terms:
(IH.8) w^w^^dJ.
Weak interactions and the breaking of hadron symmetries 11
With a suitable modification of J^ w , W^ has the propagator:
/TT CVv o (tv
\1±.7J
<7 2 ^w'
whereas the field 6
is
given
the
propagator
(III. 10)
1
d*Ml'
The coupling of W^ gives rise by itself to a renormalizable theory, provided
the \p l have spin \ or 0, similar to electrodynamics. All leading divergences,
coming from the q^q v term in the W^ propagator, are now associated with
a derivative 6 coupling. We perform now the canonical transformation:
s™
(III. 11) ^* = jexp
One easily finds:
(HI. 12) D„yt* = U tJ D li yt,
where
(111.13) D„r = drf + HgW^Ty + eA„Qu\ & ,
J? being invariant under chiral transformations, we have:
(HI. 14) JS^l/y, UB, W) = J? (V, D, y) .
We have thus eliminated from J? the dangerous field 6. On the other hand ^
is not chiral invariant, so that:
(111.15) & x {U{x)$) = expLz Jg^lj^exp iJL&Oix)] .
As explained in ref. [24], the leading weak corrections to hadron processes
are obtained considering all the graphs where a 0line starts and ends at the
same vertex. This amounts to calculate the expectation value of ^' 1 {U{x) ! ^)
in the vacuum state for 6mesons, thus defining:
(III. 16) Se x + S weak ^i = <^i(U(x) #)> .
To go further, we must specify the transformation properties of SC X . The
case where l£ x transforms as a (3, 3)©(3, 3) has been discussed in detail in
ref. [1], and yields the result quoted in Sect. 5, eq. (40). With analogous
techniques, one could treat the other possible forms for J^.
78 N. Cabibbo and L. Maiani
We are here interested in the problem whether eq. (III. 15) can give rise
to a new breaking J^ + S weak j2\ equivalent to a parity conserving one, as
was the case for the (3, 3 (3, 3).
Let us consider the case (1, 8)© (8, 1). A basis for such a representa
tion is given by a set of eight scalar and eight pseudoscalar densities a\{x)
and d\{x). We collect these densities into two, 3x3 matrices, according to:
8
D = J t d t (x)X t
The combinations:
(III. 17) D± = D±D 5
transform as the (1, 8) and the (8, 1) representations, respectively. A parity
conserving J^, would have the form:
(III. 18) J2\ = 2 Tr (DH) = Tx{D + H + D~ H) ,
H being a numerical, 3x3 traceless Hermitian matrix. Because of the
1 + y 5 structure of the current, only the D + component of <£ x is modified
by weak corrections, and eq. (III. 15) reduces to:
(111.19) ^ 1 (U(x)D)=Tr(D+exp\i 1 ^^d(x) Hexp\i^tfd(x) +D~HJ.
This means that the effect of the 0field is to impart the lefthanded part of ^
an SU 3 transformation depending upon the quantized density B(x). According
to eq. (III. 16), the modified breaking operator is to be obtained by averaging
eq. (III. 19) over the value of 6(x) in the state with no particles. One then
finds :
(111.20) Se x + S weak Se x = Tr (D+ H' + D~H).
In order for parity to be conserved, it should be possible to reduce H' to H
by an SU Z transformation. A necessary condition for this is:
(111.21) Tr {H'H 1 ^) = Tr (Hrf) .
However, one easily sees that:
(111.22) Tr({U(x)HU\x)y (U(x)H'U\x)y )<TriUHU'UH i U} ^Tr(HH f )
equality being attained if and only if
(111.23) [X\H] = 0.
Weak interactions and the breaking of hadron symmetries 79
If A 3 is given by eq. (III.5), eq. (111.23) can be satisfied either if d =
(and 6 = 0), or if H is proportional to the electric charge matrix Q (where
H'=H).
The analysis we have formally carried out in the neutral boson model
can easily be applied to the second order computation eq. (36) of Sect. 5.
One obtains again the result eq. (111.20) where:
H'= H GA 2 {[X+, [r, HJ] + [r, [A+, H]]} .
Up to terms of order (GA 2 ) 2 , one has:
(111.24) Tr (H'H")  Tr {Hit) =
=  GA 2 {Tr [H*([?i + , [r, H] + [r, [A+, H})] + h.c.} =
=  2GA 2 {Tr ([H \ X + ] [A", #]) + Tr ([# + , r ] [A + #])} =
= 2G/l 2 {Tr([r, i/]) + [r, #] + Tr([A+, /f]) + [r, H]}<0.
We note that if d ^0 the condition [A± i/] = 0, necessary to have an
equality in eq. (111.24), cannot be realized by a diagonal traceless matrix.
This proves that if Se x has a component along (8,_1)© (1, 8), parity is
violated at the order GA 2 , contrary to the case of (3, 3) © (3, 3).
REFERENCES
[1] N. Cabibbo and L. Maiani: On the origin of the weak interaction angle II, in Phys.
Rev. (to be published).
[2] M. GeixMann, R. J. Oakes and B. Renner: Phys. Rev., 175, 2195 (1968).
[3] S. Glashow and S. Weinberg: Phys. Rev. Lett., 20, 224 (1968).
[4] L. Michel and L. Radicati: Breaking of the SU 3 xSU 3 symmetry in hadron physics,
preprint (IHES and Pisa).
[5] R. P. Feynman and M. GellMann: Phys. Rev., 109, 193 (1958).
[6] Y. Nambu and G. JonaLasinio: Phys. Rev., 122, 345 (1961); 124, 246 (1961). Many
effects due to spontaneously broken symmetries (ferromagnetism, superconductivity,
superfluidity) were already known from manybody physics, but it was still not real
ized that these were different manifestations of the same general phenomenon, and
the crucial role of massless bosons was not entirely understood.
[7] S. Weinberg: Review talk, Intern. Conf. HighEnergy Physics (Vienna, 1968).
[8] M. GellMann and M. Levy: Nuovo Cimento, 16, 705 (1960).
[9] N. Cabibbo: Phys. Rev. Lett., 10, 531 (1963).
[10] For a recent assessment, see H. Filthuth: Proc. Topical Conf. Weak Interactions,
CERN (Geneva, 1969).
[11] The algebraic formulation of universality for the vector part of the current (N. Ca
bibbo: Reports of Erice School 1963) consists in requiring that the associated charge
is a wellnormalized raising operator. A complete formulation, involving also axial
current, has been given by M. GellMann: Physics, 1 (1965).
80 N. Cabibbo and L. Maiani
[12] M. GellMann: Phys. Rev., 125, 1067 (1962).
[13] D. G. Sutherland: Nucl. Phys., B2, 433 (1967) which contains references to pre
vious work.
[14] R. Dashen: to be published.
[15] S. Coleman and S. Glashow: Phys. Rev. Lett., 6, 423 (1961).
[16] R. E. Cutkosky: Particle symmetries, Reports of the 1965 Brandeis University Sum
mer Institute in Theoretical Physics (New York, 1966).
[17] L. Michel and L. Radicati: Proc. Fifth Coral Gables Conf. Symmetry Principles at
HighEnergy (A. Pearlmutter, C. A. Hurst and B. Krsunoglu eds.) (New York, 1968).
[18] N. Cabibbo: Hadrons and their interactions (A. Zichichi, ed.). Reports of the 1967
Intern. School of Physics «Ettore Majorana», Erice (New York, 1968).
[19] G. Parisi and M. Testa: Nuovo Cimento (to be published).
[20] G. Salvini: Riv. Nuovo Cimento, 1, 57 (1968).
[21] L. Bemporad, P. L. Braccini, L. Foa, K. Lubelsmeyer and D. Scmitz: Phys. Lett.,
25 B, 380 (1967).
[22] N. Cabibbo and R. Gatto: Nuovo Cimento, 21, 872 (1962).
[23] S. Coleman and S. L. Glashow: Phys. Rev., 134 B, 671 (1964); R. Socolow: Phys.
Rev., 148 B, 1221 (1965).
[24] T. D. Lee: CERN preprint 68/940/5  TH 940 (1968).
[25] See, e.g., R. Gatto, G. Sartori and M. Tonin: Phys. Lett., 28 B, 128 (1968).
[26] S. Coleman, J. Wess and B. Zumino: Phys. Rev., 177, 2237 (1969); C. Callan, S. Co
leman, J. Wess and B. Zumino: Phys. Rev., 177, 2247 (1969).
[27] E. C. G. Stuckelberg: Helv. Phys. Acta, 11, 225 and 299 (1938).
The Role of Complexity in Nature.
G. Cocconi
CERN  Geneva
1.  A common aim of people interested in science is that of improving
the comprehension of the phenomena that can be observed in the world.
It happens that the variety of the panorama that falls under our senses is
so great that the present degree of understanding is much diversified.
In attempting a classification, we tend to divide the various branches of
science into two groups: the « exact » and the « nonexact », a subdivision
that reflects the degree by which the language of mathematical analysis is
used in the interpretation. Typical of the exact sciences are astronomy,
physics, etc., while the nonexact are to a great extent the biological sciences,
the more so the more they deal with the behaviour of living organisms.
This separation, however, is not merely methodological. It also reflects
a more fundamental difference in the nature of the phenomena studied
by the disciplines that are grouped under the two labels. The exact sciences
have to deal with phenomena that, at our state of understanding, depend
on a number of characteristic variables sufficiently small to make mathe
matical methods of analysis successful in predicting new results. The facts
observed in nonexact sciences depend instead on such a complex inter
play of causes, that mathematics is often of limited help.
Thus in this context, one can say that « exact » and « nonexact » are
synonyms of « simple » and « complex », when these adjectives are used
with the meaning specified above.
In classifying some scientific activities as exact (or simple), we also yeld,
often unconsciously, to a sort of hope. The hope that many, possibly
all, natural phenomena will eventually be mastered using mathematical tools.
This hope runs all along the history of science, from the Greek philosophers
who believed that the Gods were thinking in terms of arithmetic and geometry,
to Newton and Einstein who tried to unify physics, astronomy, and cosmology
under common laws, and to presentday scientists who use quantum theories
to interpret all physical and chemical phenomena that fall under our experience.
82 G. Cocconi
In physics, we still hope that relativistic quantum mechanics and electro
dynamics will be able to give a complete description of matter, from solid
state to small and big molecules, from atoms to nuclei, from nucleons to
subnuclear particles, i.e. hadrons, leptons, and their combinations made
manifest by the study of the most energetic collisions produced either arti
ficially or by means of cosmic rays. We still hope that, once a certain degree
of understanding is reached in these fields, also the problems one meets in
other fields, even in the nonexact sciences, will slowly fall under the powerful
methods of analysis developed for the more exact disciplines. It is easy to
find in the history of science several good examples of this trend.
However, there are also cases where disciplines believed to belong to the
« simple » class were later found to be « complex ». For the ancients, the
animal and the vegetable worlds on Earth appeared as the products of a single
act of creation, while now we know how complex the path of evolution must
have been. The situation is similar for geology and astronomy, even through
many still hope that a simple « big bang » is at the origin of the whole so
called Universe. These are several branches of science whose first principles
we now understand much less than our predecessors thought they did.
The reason why I am talking about these matters here is that at the present
moment several of the scientists involved in what is considered one of the
most fundamental fields of research, the field of highenergy physics are begin
ning to ask themselves whether the complexities that become more and more
manifest as the properties of matter are analyzed with higher spatial and
temporal resolution could lead this branch of fundamental physics to a point
where it becomes impossible to pretend that this discipline can be classified
as exact.
Before further elaborating this point, I will try to qualify the meaning of
the term « nonexact » attributed to a branch of science. A concise definition
is the following: Complex disciplines are those obeying laws that evolve
historically.
One must be aware of the fact that what makes our definition of complexity
defy mathematical analysis is the word « historical ». This is because history
contains the idea of the « arrow of time », a concept absent in all fundamental
laws of physics that can be expressed mathematically.
The classical example of historical evolution is that postulated by Darwin
in order to understand the origin of life on Earth. We now know that all
history of living organisms progressed via a string of processes, each a con
sequence, a chance consequence, of the previous one, and that a modifica
tion introduced in a step by a physical or chemical reaction had consequences
that depended on the preceding history. In biological evolutions there is
no means of going backwards to recreate the conditions that were present
The role of complexity in nature 83
at an earlier stage. This is the reason why the laws that govern life on Earth
today are different from those that governed it yersterday and also from
those that will govern it tomorrow.
It is illuminating to realize that in order to give an « exact » reason for
the concept of the unique direction of time it is necessary to bring into the
picture an evolving system. In physics, there is no way of understanding the
existence of the arrow of time if one remains within the framework of the
fundamental laws of quantum mechanics, which are time symmetric.
As pointed out by Gold, time asymmetry is created by the fact that the
space around us acts, for the energy radiated into it, as a cold sink. Energy
emanated from any reaction is lost into space, never to be returned. Time
points in the direction corresponding to energy dump, a direction that is de
termined by the way in which the world around us evolved and is evolving.
In our context, the most important peculiarity of evolution is that, in the
complex situations where it works, it has the possibility of creating at each
instant of its development the laws that govern it.
For example, the way in which living matter organized itself in the early
reducing atmosphere present on the Earth, was very different from the way
in which it evolved later when the atmosphere became oxidizing because of
the existence of life.
It is this possibility of selfregeneration, coupled with the chance that
enters in each step, that makes historical evolution so powerful in creating
new possibilities, actually new laws.
Now, the question is the following: can this kind of insight that we
have gained from the nonexact disciplines be of help in developing further
understanding of the « exact and simple » world of physics ?
What is the consequence of evolution, of the arrow of time, in establishing
the fundamental laws, the exact and simple laws of quantum physics ? Those
who think that this way of arguing is sacrilegious may indeed be right; how
ever, they should be reminded that, when the arrow of time was not recognized
to be operating in the biological sciences, the living world was considered
static, dominated by fixed laws, apart from an act of creation that defied
definition. And it made sense.
In physics now we are in about the same situation; we have some fun
damental immutable laws to which all mechanical facts obey — conservation
of energy, conservation of charge, constancy of velocity of light, etc., etc.,
and far back in time, ten billion years ago, some big event that put all this
world into being. We accept the existence of an arrow of time, but we relate
it to an inevitable emptiness of the space around us. Could it not be that
this static conception is wrong, as was that of the biologists before Darwin ?
In the following pages I will try to show that such a possibility exists, and
84 G. Cocconi
that complexity, far from bringing confusion, could in fact open vistas that
our present culture has some tendency to dismiss.
2.  Having stated our aims, let us look at the causes of complexity and
try to establish a correlation between complexity and the property of the
simplest phenomena of which complexity is built. It is found that outstanding
correlation exists between complexity and the sign of the energy balance of
the elementary reactions. Complexity invariably arises when the simplest
reactions become endothermic, i.e. when energy has to be supplied to the
evolving medium. The worlds of molecules, of atoms, of nuclei, as well as
that of planets, stars and galaxies, are « simple » worlds only when exo
thermic reactions take place in them.
Consider the case of nuclei. The building of heavier nuclei starting from
lighter ones is exothermic only up to iron, then becomes endothermic. if the
Coulomb repulsion is not circumvented. As a consequence, the formation
of nuclei up to iron is easily achieved in the laboratory via collisions of two
bodies and in nature through the slow burning of light nuclei in stars, as in
the sun. However, the formation of heavier nuclei, like lead, uranium and
beyond, asks for a lot of ingenuity on the part of nature. We now believe
that it can be achieved through the very intense neutron bombardment
(to overcome Coulomb repulsion) that can take place in rapidly evolving
matter, but it is not yet clear whether these conditions can be found in a
collapsing supernova or in the big bang (again!) that presumably took place
ten billion years ago. In the laboratory, the heaviest nuclei have been ob
tained, so far, only via the bombardment of already existing heavy nuclei;
never by bringing light nuclei together.
Also the astronomical world is simple, beautifully simple, only when
bodies at great distances from one another, placed there by a still unknown
mechanism, slowly dissipate their gravitational energy to form planetary
systems, streams of stars rotating into a galaxy, or nebular matter on the
way to condensing into proto stars. The endothermic process that brings
all this into being is certainly not simple, be it the initial big bang or the con
tinuous creation of matter of the steady state.
An even better r story is presented by molecules, whose behaviour we
are able to follow without interruption, from the simplest exothermic two
body reactions of inorganic chemistry, to the great organic constructions
kept alive by the continuous flux of energy that, on Earth, comes from
the Sun.
These examples, besides illustrating how complexity needs an energy
source, also show that, for building elaborate structures, it is necessary
to have a medium where manybody reactions can take place within times
The role of complexity in nature 85
short in comparison with the disintegration lifetimes. On Earth, the molecules
had the opportunity of arranging themselves into the long chains that even
tually led to DNA, in the warm broth imagined by Oparin, where the products
of the reactions ocurring in the atmosphere and on the surface could meet
and react; a process that is going on even today, within the living organisms,
and is made manifest by mutations.
These considerations are of importance for highenergy physics because the
most characteristic property of elementary particles is that they are all produced
via endothermic reactions. In classical nuclear physics the energetic particles
produced by accelerators were used either to make stable structures or to
overcome Coulomb repulsive barriers in order to add some nucleons to already
existing nuclei, all exothermic processes. Today in highenergy physics the
accelerators are used in a different way, namely to supply to the known stable
particles the energy necessary to build more complex, heavier states, which
require energy to be created. The socalled elementary particles obtained in
this way, mesons and baryons, are thus the product of endothermic reactions,
are heavier than the sum of the masses of their constituents and, consequently,
have in general very short disintegration lifetimes, down to 10~ 22 s. Though
the number of these particles is already quite large— more than one hundred —
and their masses are as high as about three proton masses, we do not have
any indication that particles of much higher mass cannot exist, albeit for short
times. The present limitation in the number of particles reflects only the
present maximum energy of the accelerators. Highenergy physicists are
convinced that as soon as larger accelerators are built, particles of larger
masses will be discovered, having disintegration lifetimes not shorter than
those already known today.
In these circumstances, it becomes legitimate to ask whether situations
could occur capable of bringing to the most fundamental branch of physics
developments resembling those so far observed only in nonexact sciences,
the developments produced by complexity.
Thus, there are similarities between the world of elementary particles
and that of molecules; both depend on the occurrence of endothermic pro
cesses and for both there is the possibility of building complex structures
using simpler building blocks. How far one can build with elementary par
ticles is not known, but so far no limits have been felt, either. Actually,
as long as we create particles as we do now, one by one, by bringing
together two simpler particles and hoping that by hitting each other at
great speed they will somehow coalesce, there is a drastic limit to the com
plexities that can be built. In the case of molecules, the progress would have
been very limited indeed if chemists could produce compounds only by
shooting together a pair of atoms or simple molecules. The building of
86 G. Cocconi
more elaborate structures requires the myriad of collisions taking place
in a gas, in a solution, and, very important, the presence of catalysts that
can keep alive intermediate steps. One needed the primitive oceans and
billions of years in order to have the chance of creating the molecules of life.
Of course, one also needed the practically inexhaustible possibilities of the
carbon bonds, but can we say now that equally far reaching possibilities do
not exist in structures composed of elementary particles ?
This doubt makes it legitimate to speculate in which circumstances the com
plexities of elementary particles, if virtually possible, could become manifest.
In the world as we know it today, it appears that the spontaneous evolu
tion of matter we are talking about can be induced only by gravity. Gravity is
the only known force that does not saturate, i.e. does not cease to operate
when many field sources are brought together, contrary to what happens for
electromagnetic forces, weak coupling forces and molecular forces. The pull
of gravity steadily increases as more and more matter is brought together.
Just as nuclear reactions start when enough matter is condensed in a star, it
is conceivable that the exothermic reactions of hadronic and leptonic matter
will fully develop their possibilities only when large enough masses will com
press matter to the point where the characteristic energy per particle is well
above the giga electronvolt. In matter consisting of baryons compressed to de
generacy by gravity, the characteristic momentum per particle kpc ~ 10 3  8 @*eV,
where q is the density in grams per cubic centimeter. Already at the density
of neutron stars (g c± 10 15 gcm~ 3 ) momenta up to ~ 1 GeV are available;
these are also the densities of matter in nuclei. The places where these densities
can be exceeded are those where matter condenses even further: in the col
lapsing neutron stars and possibly in galactic centres. It is not surprising
by chance that at present we have no way of telling what the behaviour of
matter is in these bodies.
In the laboratory, present knowledge about the interactions of nuclei with
giga electronvolt particles derives exclusively from the study of twobody in
teractions and it can be easily predicted that much more complex situations, if
they exist, will not be observed as long as we continue to use this simple channel.
A practical way of partially circumventing this limitation, short of creating
the concentration of energy possible for astronomical bodies, is perhaps to
use the collisions between particles and nuclei, and between nuclei and nuclei
at effective energies (i.e. centreofmass energies between composite structures)
of several giga electronvolts. Until now, particlenuclei interactions have
been studied at high energy only to gather information about the socalled
coherent or diffraction dissociation reactions, where the nucleus acts as a single
particle. The complex reactions we are looking for should be observed in the
incoherent background, where the complex structures built by the collision with
The role of complexity in nature 87
the first nucleon have the chance of interacting further before leaving the nucleus.
With the present accelerators, the energies available are not yet suffi
ciently high. Only with the new generation of 100 to 500 GeV accelerators
will one obtain secondorder collisions within the same nucleus with total
cm. energies of many giga electronvolts. The best conditions in this respect
will undoubtedly be obtained with colliding beams of nuclei.
Large Lorentz factors for the complex structures built in these collisions
are necessary not only to make available the energy needed for carrying out
the endothermic reactions, but also for bringing together these unstable
structures before they decay. Even if widths of the order of a few 100 MeV
continue to be characteristic, mean decay paths equal to nuclear dimensions
demand Lorentz factors larger than ten.
3.  It is appealing to think that in the realm of high energies, situations
could develop similar to those possible for molecules, and that subtle and
apparently insignificant details of some interactions could have unimaginable
and radical consequences in the historical evolution of matter.
Clearly, the only justification today for this kind of science fiction is the
observation of a great variety of endothermal highenergy reactions, a phe
nomenon that has some parallel with the molecular case.
It should be realized that if such a possibility really exists, our concep
tions of the physical world would be greatly affected.
The immutable laws of physics could become as « ephemeral » as those
of organic life, immutable only for observations limited in space and in time,
and even more exotic, the evolution of these laws would depend on history,
a history that has followed a path that, to a great extent, must have been
determined by chance. Seen from this point of view, even the Heisenberg
uncertainty principle could be considered a temporary consequence of laws
establishing themselves in an undeterminable manner.
Another kind of life, the life of the physical world, would then be developing
around us, in parallel with that we are accustomed to call the real life, that
on Earth, of the organic world.
Is the history of organic life a subset of the more general history of the
physical world ? Has the evolution of organic life the possibility of interfering
with the evolution of the physical laws — and vice versa!
I realize that I have carried the argument to its extreme consequences and
beyond, into the metaphysical sphere. But to me, it seemed useful to emphasize
how complexity can have peculiar ways of manifesting itself through the
possibility of developing momentous consequences from details apparently
of no importance.
The highenergy phenomena, as we know them now, seem to have prop
erties that could give rise to complexities of this kind.
Channeling of Ultrarelativistic Charged Particles
in Crystals.
B. Ferretti
CERN  Geneva
When very high energy charged particles (usually electrons) or gamma
rays pass through crystals, the coherent interaction with the lattice gives rise
to several interesting phenomena, which have been studied both theoretically
and experimentally in recent years [1].
There is an aspect of these phenomena, which until now has not been
investigated experimentally, because it becomes important at energies higher
than those actually at hand, and which, as far as I know, has not received
either much theoretical attention, with the exception of a stimulating paper
by Schiff [2]. We have in mind the fact that, in appropriate circumstances,
the interaction between lattice and charged particles becomes so strong that
the Born approximation, usually quite valid in the electrodynamic case at
very high energies, has to break down completely [3]. This breakdown can be
attributed to two circumstances: First, the fact that a description of the
electrons wave functions by means of plane waves becomes very inadequate;
and, second, the fact that the coherent emission of many quanta, or even a
« coherent cascade » may become important.
The resolution of the problem of finding a more adequate solution for the
motion of very high energy electrons in crystals is preliminary dependent
upon the investigation of the « coherent cascade ». This short note contains
a few results obtained in trying to solve this preliminary problem.
What we have in mind to discuss particularly is the possibility of « chan
neling » of very high energy electrons, or, better, positrons, around certain
directions in a crystal.
We shall consider, for simplicity, a cubic lattice, having the principal
crystallographic axes along x, y, z and a particle traveling around a direction
making a very small angle with the x axis. More precisely, if p x , Py, Pz are
the component of the momentum of the incoming (free) particle, we consider
Channeling of ultrarelativistic charged particles in crystals 89
the case in which
(1) #z>/V>/>z — °
Then, it might be shown [4] that the wave function of the electron inside
the crystal can be suitably approximated by:
(2)
where
4 v
= A exp [ipx] y E ,* E n z) exp i V5 JVE'V(yz') dz' J Xa (?) ,
2
E' = Ep^ c=l;K=l,
2p
E is the energy of the particle, p is the component of the Bloch momentum
along x (p c^px), m is the mass of the particle, V(y, z) is the average of the
potential of the crystal, taken along the classical path in a cell, and the func
tion Xa( z ) satisfies the equation
(3) xte) + 2p(E a VWi)Xa = 0>
where V(z) is the average of V(x, y, z) in the xy plane. Inside the crystal,
in place of eq. (1) we shall have
(1') p^V2pE'^>V2pE a .
If a is the pitch of the lattice, V(z) might be quite well represented by
(4) V(z) = F (exp [ zfs ] + exp [ (a  z)/s ]) 0<z<a
where
s = aJZi,
a is the atomic Bohr radius and Z is the atomic number of the element which
is supposed to form the crystal.
In the case of the positron (which is the most interesting for the reason
that we shall see) the channeling is important when
(5) Ea « V .
In this case we see immediately, considering eqs. (2) and (3), that the
positron can be trapped between two nets of equilibrium positions of the
nuclei of the crystal. The planes % and n 2 of these nets are obviously orthogonal
90 B. Ferretti
to z. In this case it is quite clear that the particle might be channeled in a
small neighbourhood of directions belonging to these planes. This channeling
however can be disturbed by several effects, as the interaction with the elec
trons of the crystal, the effect of the zero point, and thermal motion of the
atom, and so on.
If E a is not much less than V , the most disturbing effect will be, in general,
the interaction with the zero point and thermal motion. It is this effect which
we have particularly tried to estimate.
To arrive at expression (2) for the wave function of the positron one has
essentially to use the fact that the potential of the lattice is periodic, and that,
for the particular solution which we are considering, the frequencies of the
components of the forces along x and y are very different. In this way, for
instance, the forces along y can be considered as an adiabatic perturbation
for the motion along x.
These circumstances allow us to separate approximately the variables
in the solution of the equation of motion, and to arrive at expressions (2)
and (3).
If. however, one takes into account the zero point motion, the perturba
tion due to the displacement of the lattice atoms will not be almost periodic,
and consequently the separation of the variables will be no longer pos
sible.
A preliminary estimate, however, shows that if condition (5) is satisfied,
the effect of the atom motion is very small, in such a way that it can be con
sidered as produced by a small perturbation AK This perturbation A V will
be a functional of the operators u x (x n , y m ), u 2 {x n ,y m ) which describe the
displacement of the two nets ti 1 , tc 2 . (x n and y m are the coordinates of the
equilibrium positions of the atoms belonging to n^) (*)
1 v ■
=^,— ? (exp [iqx]a qj + exp [— iqx]a qi ) ,
VlNMv <»q
where M is the atom mass and TV is the number of atoms for unit voume.
Only the atoms, however, which are nearest to the classical trajectory can
contribute appreciably to AV. For a given classical trajectory and for any x n
there will be in general one (or in exceptional cases, that we shall disregard,
at most two) of such atoms belonging to ji x ; and similarly, for any x' n , one
belonging to n 2 . The « effective » displacement operators u x and « 2 therefore,
might be considered as functions of a parameter only. Furthermore, the
(*) a , and a Qi in the « x expression are the usual annihilation and creation operators
Channeling of ultrarelativistic charged particles in crystals 91
correlations of the orthogonal component of the displacement will not be
important for determining AV when eq. (5) is valid.
For these reasons we might use as well a twodimensional, instead of a
threedimensional lattice, for studying the effect of the random motion of
the atoms on the channeling. The wave equation then will be
(6) (~ + ^) V>(*. z) + [£ 2  m 2  2E(f(z) + AK(*, z))] y(x, z) = 0,
where
,r,^ K^r *r I \~ z\uXx) f a — zl w 2 (x)\
AV is obtained by expanding the potential V in powers of the displacements
% and w 2 .
The solution will be written in the form
(6") y> = if a + Ay ,
where
exp [ip a x]
Wa = — —=—% a {z),
A W=2,c b (x)y b ,
E =p a + AE a =p b + AE b ,
L being a normalization length.
We can then solve our problem in the Born approximation with respect
to the perturbation AV, in order to find the probability of transition for
unit path, from any state ip a to any state ip b . This probability of transition
is given in the usual form
(7) P a M, "2) = 2?r (y a A*> 6 ) 2 e ,
where q = L/2ti is the density per unit energy of the states exp [ipx]fVL.
We are of course interested in the average value (with respect to the motion
of the atom) of this probability transition
0') P ab = <\(y a \AV Wb )\*yL.
The evaluation of <(^JAK^ & ) 2 > can immediately be performed, and one
92 B. Ferretti
obtains :
<WAF n )«>=^
o i r . r z i j i 2
rg!J^ exp [d^ d 1 ■
o
1 . y J_  sin(/(/7 & — /? g )+gliL)
2NM
i(PbPa) + tf
1
1 — exp [— coJkT]
+
+
sm(\i(p b —p a ) — q\$L)
\i(Pb—Pa)—q\
exp [— co q fkT]
1 — exp [ — wJkT)\ '
where i is a unit vector parallel to x.
Using the Debye approximation, in the case in which r=0 we obtain
(8)
P ab —
71
16
^^{M'fe)
2 / t; \ 2 ^71d/u — i? & — /? a 
kTvM
if \Pb—Pa\< —
if 1^6— A»l>
&r D
(v is the sound velocity and T D the Debye's temperature).
Before using the result (8) we have to discuss the consistency of this result
and the conditions under which it is valid. The undisturbed particle classically
travels between n x and ji 2 , oscillating along z. During a complete oscillation
it travels along x a length x (x~p\dz/V2p(E a —y), where z is the clas
sical amplitude of oscillation I.
For the consistency of our results it is necessary that
(9)
b
The condition (9), together with the condition that the quantum numbers
of % a and % b are not too small, is also sufficient.
In fact, if we follow our particle for a path x > x, due to the random
ness of the perturbation V, the states will no longer be a coherent super
position as in (6"), but a statistical superposition of incoherent states.
Let p b be the probability of any pure state tp b . Then, in place of the wave
equation (6) we have to consider the diffusion equation
(10)
&Pa
dx
J,Pab(Pb
b
■Pa)>
Channeling of ultrarelativistic charged particles in crystals 93
which may be considered valid with P ab = P ba given by eq. (8), until the
condition (9) is respected for all the states for which p a is appreciably different
from zero.
We can give some order of magnitude: If
p = 10 10 eV ,
V = 150eV,
Fo/M = 0.6xlO 9 ,
v =10" 5 ,
A:r D /^=3xl0 3 eV/c,
a = 3 x 10~ 8 cm ,
2z 0a =0.6«,
2z 0b = 0.75 a,
one has:
P aa x^lO~\ P ab x~lO*, lP„ c x10
Leaving the other data unchanged, and taking z 0a = 0.25«, the mean
free path for the diffusion of a particle which is initially in the state a will
be of the order of one centimeter or more. In these conditions the scattering
against the electrons might become more effective in destroying the channeling
than the zero point motion. Obviously, in the case of incoming electrons,
on the contrary, the zero point motion will be always very effective in destroying
the channeling, because they would be trapped around the equilibrium posi
tion net of the nuclei, and not between two nets of equilibrium positions as
it happens for positrons.
Returning to positrons, of a beam impinging on the crystal, one half will
have a « collision parameter » such that z Qa < 0.25a. The condition on the
incidence angle ■& with the xy plane is much more restrictive: for/? =10 GeV,
# ~ 10 5 rad.
The resulting restriction in the phase space of the incoming particle is
however largely compatible with the indetermination principle.
One can now ask whether our results can be generalized to cases in which
the condition (1') is not satisfied. One might investigate whether, for instance,
the trapping can arise between parallel crystallographic planes different than
those which we have previously considered.
Now, an immediate generalization of the preceding analysis shows that
a necessary condition for the smallness of the zeropoint motion perturba
tion is that the distance between neighbouring planes which are supposed to
trap the particle is great compared to VTJiSkTvM). This condition rules
94 B. Ferretti
out almost all the possibilities, with the exception of the planes for which the
Mill indices can be very small numbers.
When the very severe restriction for trapping are not satisfied, the scat
tering will not be very different in a crystal or in a corresponding amorphous
material.
Concluding, we remark that it is perhaps possible either to use the chan
neling phenomenon which we have discussed for collimating very high energy
positive particles, if one can obtain suitable crystals, or to use the channeling
for studying very rare imperfections in almost perfect crystals by means of
very high energy positive particles.
REFERENCES
[1] A rather complete list of references about this topic can be found in the report by
U. Timm: Coherent Bremsstrahlung of Electrons in Crystals, DESY, 69/14 (March 1969).
[2] L. I. Schiff: Phys. Rev., 117, 1394 (1960).
[3] B. Ferretti: Nuovo Cimento, 7, 118 (1950).
[4] See, for instance, the notes of the lectures given in 1969 at CERN, about The Brems
strahlung in Crystals.
Experimental Work on Coherent Scattering
of HighEnergy Hadrons by Light Nuclei.
G. Fidecaro and M. Fidecaro
CERNTrieste HighEnergy Group  Geneva and Trieste
1.  Introduction.
In the last few years, several measurements [119] have been performed
in order to study the coherent scattering of highenergy hadrons from light
nuclei. We intend to present here the results so far obtained, including those
contributed, in the case of the deuterons, by the CERNTrieste HighEnergy
Group. A summary is given in Tables IIV.
Various techniques (emulsions, bubble chambers, counters, and spark
chambers) have been used, as expected from the fact that the crosssections
involved vary by some orders of magnitude when the momentum transfer
to the target particle is increased. Typically, in the pd case, at 13 GeV/c,
the crosssection decreases from 0.3 b/(GeV) 2 in the forward direction, to
0.1 [xb/(GeV) 2 for \t\ = 1.8 (GeV) 2 . Moreover, a good precision in the deter
mination of the kinematics of the events is of great importance for this type
of experiments: an accurate reconstruction of the events in fact, on one
hand helps to select the collisions which leave the target nucleus in the fun
damental state, on the other hand it provides the /resolving power required
to search for a possible structure in the differential crosssection.
All the experiments but one [3] cover a limited angular region in the
forward or backward direction and, correspondingly, two different kinds of
phenomena are studied.
Concerning the forward scattering region, in the first place these experi
ments give information on the structure of light nuclei. The use of strong
interacting particles which have a non negligible probability of colliding at
least twice with nucleons when traversing a nucleus, allows one to obtain
results complementary to those obtained in the case of electron scattering,
where the scattering amplitude depends predominantly on the singleparticle
96 G. Fidecaro and M. Fidecaro
Table I.  Coherent (elastic) scattering of highenergy hadrons by light nuclei: a) protons.
Momen Momentum
turn transfer
(GeV/c) (GeV/c) 2
Technique used
Authors
cm.
(degree)
pd
p 12 C
p 16 Q
1.70
2.78
4.85
6.87
8.89
10.90
2.78
1.70
12.8
p 4 He 1.2
1.7
1.7
1.7
0.003 < — /< 0.2
0.44 </<1.54
0.026<f<3.44
0.2 < — /<!.
0.007<f<0.7
Emulsion to record the slow
recoil deuterons from a tar
get of deuterated polyethy
lene  AE/E~2.5^5%
Scintillator telescopes for both
the proton and the deuteron;
magnetic analysis and TOF
measurement in the dbranch
a) pbranch: magnetic spec
trometer (wire spark cham
bers), AE = 3 MeV, and
TOF measurement
b) dbranch: range spectro
meter
Scintillation counters and wire
spark chambers, At It — 2%
pbranch: scintillator range te
lescope, A£'<20MeV
N. Dalkhazhav et 4.1^ 15.6
0.007< — f < 0.47  pbranch : magnetic spectrome
ter (wire spark chambers),
I AE = 3 MeV, and TOF
measurement
0.023 <?< 0.208
0.009<*< 0.509
al. [1], JINR
Proton Syn
chrotron
E. Coleman et
al. [2], Cos
motron
G. W. Bennett
et al. [3],
Cosmotron
3.1^ 15.6
2.4
1.4
1.4
1.2
29.0
9.3
12.6
8.9
8.2
55.0
10.0^170.0
CERNTrieste [4] 7.8^ 23.1
5.4^ 58.4
E. T. Boschitz et
al. [5], Virgi
nia University
H. Palevsky et
al. [6], Cos
motron
6.9^ 58.1
6.0^ 18.0
3.5^ 27.3
density. This is equivalent to saying that by using a hadron probe it is pos
sible to study nucleonnucleon correlations inside a nucleus [20].
There is also a specific interest which concerns the hadronnucleon ele
mentary interaction. At high energy ( > 1 GeV/c) the probability of having
a single hadronnucleon elastic collision decreases strongly when the mo
mentum transfer is increased, while, as it will be seen later, the probability
for a double collision decreases less fast; that is, it is easier to obtain a large
transfer of momentum by means of two subsequent collisions than by means
of only one ; and there exists a ^interval for which the two probabilities are
nearly equal. This region, in which the two scattering amplitudes interfere,
is sensitive to the phase difference between the single and the double scat
Coherent scattering of highenergy hadrons 97
Table II.  Coherent {elastic) scattering of highenergy hadrons by light nuclei: b) pions, kaons, deuterons.
Momen
Momentum
tum
transfer
c.m.
(GeV/c)
(GeV/c) 2
Technique used
Authors
(degree)
K+d
3.65
0.05 <
?<0.90
20 in. deuterium bubble cham
ber
H. C. Hsiung et
al. [7], BNL
8.0
33.5
6.0
0.03 <
?<0.21
81 cm deuterium bubble cham
ber
Scintillator hodoscopes for nd
CERNSaclay [8]
4.5
12.0
7rd
2.01
0.262<
/< 0.878
R. C. Chase et
26.1
48.9
3.77
0.282<
f< 0.898
angular correlation; TOF
al. [9], Argonne
18.1
32.7
5.53
0.291 <
/< 1.232
window in the dbranch,
sweeping magnets in 7t and
d branches to decrease the
background
14.7
32.6
0.895
0.165<
/< 0.940
Wire spark chambers for Trd
CERNTrieste [10]
37.2
99.0
0.994
0.17 <
/<0.46
angular correlation, At/t~
CERNTrieste [11]
34.8
70.5
9.13
0.20 <
?<2.3
~ 2%; dTOF correlated (or
CERNTrieste [12]
9.3
21.0
13.0
0.20 <
f<0.57
not) with pion angle keeps
7.5
12.5
15.2
0.20 <
f<1.02
down the background
7.0
15.8
K~d
3.0
0.27 <
/<0.175
81 cm deuterium bubble cham
ber
W. Hoogland et
al. [13], CERN
6.5
16.5
dd
2.2
0.05 <
/<1.9
Deuterium bubble chamber
M. Bazin et al. (pre
7.9
0.05 <
/<0.7
liminary results 
private commu
nication)
Table III.  Coherent {elastic and quasi elastic) scattering of highenergy hadrons by light nuclei.
Momentum
Momentum transfer
(GeV/c)
(GeV/c) 2
Technique used
Authors
Pd
1.29
7.0xl0" 4 < — /< 8.0 xl0~ 3
Magnetic spectrometer, with
L. M. C. Dutton and
1.39
8.0xl0~ 4 <f< 9.5 xlO 3
sonic spark chambers,
H. Buan van der
1.54
9.5 x 10" 4 <  /•< 12.0 x 10 3
A^ = 0.5%
Raay [14]
1.69
1 1.0 xl0 4 <*< 14.0 Xl0~ 3
19.3
1.6xl0 3 <r<0.1
Magnetic spectrometer, with
sonic spark chambers,
G. Bellettini et
al. [15a]
p 6 Li
19.3
/<0.1
Aplp = 0.5%
[15a]
7 Li
19.3
f<0.1
[15a]
Be
19.3
?<0.1
[15a]
C
21.5
/<0.12
G. Bellettini et
al. [15b]
98 G. Fidecaro and M. Fidecaro
Table IV.  Coherent (elastic) scattering of highenergy hadrons by light nuclei (backward).
Momentum
(GeV/cm) Technique used
Authors
(degree)
Pd
1.70
2.03
2.25
1.41
1.70
2.40
2.65
1.37
1.70
2.78
4.50
4.25
1.9
1.7
Scintillator telescopes for both the proton
and the deuteron; magnetic analysis
and TOF measurement in the dbranch
Scintillator telescopes for both the proton
and the deuteron; range analysis (op
tical spark chambers) in the pbranch;
magnetic analysis in the dbranch
Scintillator telescopes for both the proton
and the deuteron; magnetic analysis
(kp/p = ± 2%) and TOF selection in
the dbranch. (The reaction studied is
dp > dp)
E. Coleman et al. [2]
152.1^120.0
BNLCosmotron
153.5^117.3
154.0M20.0
N. G. Birger et al. [16]
152
151
149.4
147.5
Yu. D. Bajukov et al. [17]
160
159.5
162
165.5
Yu. D. Bajukov et al. [18]
145
ITEF Proton Synchro
tron (internal beam,
CD 2 target)
J. Banaigs et al. [19],
174.5^180
Saturne
G. W. Bennett et al. [3], < 170
BNLCosmotron
tering amplitudes; if, as it happens generally at highenergy, both the am
plitudes are purely imaginary (high absorptive process), the interference is
destructive and the differential crosssection goes down to zero (*).
If the ratio between the real and the imaginary part of the scattering
amplitude is different from zero, the crosssection will show a more or less
pronounced minimum; one could hope to evaluate from the depth of this
minimum the dependence of the real part of the scattering amplitude on
the momentum transfer, which at high energy cannot be obtained in any
other direct way [21]. This is a case in which nuclear physics comes to help
elementary particle physics.
It is perhaps worth recalling also that attempts have been made to in
terpret the forward scattering of hadrons by nucleons in terms of a model
(*) A similar situation arises when one compares the probability of a scattering of
order n, with the probability of a scattering of order (w — 1). This leads to a typical dif
fraction pattern.
Coherent scattering of highenergy hadrons 99
which treates the target particle as a composite system. The nuclear cross
sections show indeed a t (or «) dependence very similar to the one observed
when the scatterer is an elementary particle [22].
Concerning the backward scattering region, the present tendency is to
try models in terms of Feynman diagrams with exchange of baryons. How
ever, the phenomenology is in a much more rudimentary stage and the ex
perimental work still very much incomplete.
The progress made in the field of hadron scattering by light nuclei comes
both from development of the Glauber model [23] of multiple scattering
which tends to explain satisfactorily the forward scattering, and from the
new technical developments which have allowed experimental physicists to
perform measurements of very small crosssections, thus making possible
the continuous comparison and the improvement of the theory. The exist
ence of these new techniques, in particular, will certainly shed light and in
duce progress in the phenomenology of backward scattering.
2.  The forward scattering region.
The formulae given below have been derived [23, 24] in the limit of the
highenergy approximation and of very small forward angles, i.e., one as
sumes that the wavelength of the incident particle is small in comparison
to its range of interaction and that the angles considered correspond to the
angular region near the forward diffraction peak.
In this approximation the elastic scattering amplitude for the case of two
colliding particles is given by:
(1) f(k\k) = ^Jexp ft** 1 ) A][lexp[i*(*)]]d*A,
where k and k 1 are, respectively, the initial and the final momentum of the
incoming particle in the laboratory system, and b = UJ + ) is the impact
parameter. The term %{b) is a complex phase shift which in the case of
spherically symmetric interaction is related to the betterknown phase shifts
of the partial wave analysis through the formula
m = x{^Y L ) = u l
Formula (1) is valid for a spinindependent interaction of an arbitrary
shape. It has been obtained by using the approximation P z (cos0)»/ o (6V— ?,)
where — t is the fourmomentum transfer, and by replacing the sum over /
with an integral over b.
100 G. Fidecaro and M. Fide car o
The next step is to consider a system of A particles bound to form a
nucleus. The approximation is here made that the single nucleons are frozen
in their instantaneous position r x , ...,r A during the time that the incoming
particle goes through the nucleus. The generalization of expression (1) is
(2) F{q) = A Jexp fa.A]d*A<v>lexp [ X (b, r lt ..., rj]y>> ,
where q = k— k 1 and \q\ 2 = — t. It is here that the most critical hypothesis
of the model arises; that is, the phase factor x(b, r i, •■•,r A ) is assumed to
be the sum of the individual phase factors
A
X(b, r lt ...,rj) = ^XiiP—Si) ,
ii
sj being the component of r t along the incident beam. As a result,
(3) F(q) = ~ Jexp [iqb]d*bjd\ ... d 3 ^^*(r l5 ..., O^QS^)'
{ln^^Jexpt^Aj^/^Odv)]^!,....^).
A
If one expands JJ, the scattering amplitude F can be represented as a
ii
polynomial in the hadronnucleon scattering amplitude fj(q). This poly
nomial is interpreted as a sum of terms originated by multiple scatterings:
first, second, ... order term corresponds to a single, double, ... scattering;
the highest term is of order A, which is a consequence of the fact that the
Glauber model takes into account the multiple collisions just by adding the
phase shifts.
Various attempts [2528] have been made to improve the Glauber model
by dropping some of the approximations. However, it appears to be a
delicate matter to introduce new corrections; for instance, in the case of
the deuteron, Harrington [29] has shown that in some cases the offshell
contributions cancel the sum of all the higher order terms. On the other
hand it is a fact that the experimental values for the crosssections obtained
until now, with the exception of the ones in a very backward direction, are
fitted in a reasonable way if the scattering amplitude is given by eq. (3),
with (d<r/d£),.,.= Fte) 2 .
In most of these fits [30] the hadronnucleon scattering amplitude which
Coherent scattering of highenergy hadrons 101
appears in formula (3) has been parametrized as
0V
f(q)= 4^0 — *"*)exp
as suggested by the available experimental data, where a is the hadron
nucleon total crosssection, and a is the ratio between the real and the
imaginary part of the scattering amplitude. In some cases more accurate
amplitudes were used, when available from phaseshift analysis of experi
mental data [27] or from extrapolation to high energy via finite energy sum
rules [27, 31].
Concerning the wave function ip(r x , ..., r A ), the experimental information
is rather accurate in the cases where A < 3, at least for values of r not too
small, while for A>4 particular models have to be taken.
Czyz and Lesniak [32] have computed formula (3) by using an inde
pendent particle model and a Gaussian dependence on r for the single par
ticle density. The nuclear scattering amplitude is well approximated by
F(q)
ik_
2ti
(R 2 + 2£ 2 ) exp
mo
l) m .(l
/ay
\27z(RZ + 2pz)) eXP
(R 2 + 2fi 2 )q 2
4/
R being the width of the singleparticle density distribution. This fomula
shows that if the hadronnucleon amplitude is purely imaginary (a = 0),
the nuclear amplitude F{q) is also purely imaginary, and the double scat
tering term (j = 2) has opposite sign to the single scattering term (j =1),
and half its slope ; for the value of the momentum transfer at which the two
terms become equal (in absolute value) the crosssection goes to zero, as
mentioned in Sect. 1. This happens, when
t n =
(R 2 /2 + £ 2 )
In
£(*+'):
In a similar way other (A — 2) minima would arise. If a ^ the dip will
be filled up fast when a is increased, while the other parts of the curve are
rather insensitive to this parameter.
3.  The hadrondeuteron scattering.
Among the experiments already mentioned, the hadrondeuteron scat
tering should be the simplest one from the point of view of the analysis,
102 G. Fidecaro and M. Fidecaro
because only two nucleons can be involved as scatterers. This advantage
is partly counterbalanced by the fact that the deuteron is a spinone par
ticle. For unpolarized deuteron targets, the observed crosssection is the
average of that found for the three states of polarization [33]:
(SKi. <mW)m>i
The operator F(q, S) is a linear functional F(q, S) = F x {q, S) + F 2 (q, S) of
the form factor operator S, which is a linear combination of the scalar form
factor S and of the quadrupole form factor S 2 . Operators F x and F 2 rep
resent the single and double scattering, respectively,
*i(a, S) =A(q)S(q[2) + Mq)S(q/2) ,
and
^^=44HWf+^(f*')+^(f^(f*')
c I [/ 1 (f + ,')/ 2 ( + <)][/ 1 (.)/ 2 (^)]) d v,
where f x and f 2 are the elastic scattering amplitudes for collisions between
the hadron and particles 1 and 2 of the deuteron. The coefficient C\ is 1
if the incident hadron has isospin \, and is \ for an incident hadron of unit
isospin.
By choosing, for instance, a polarization axis along q, one observes by
developing the above formula that only the double scattering can contribute
to the spinflip transition Am = ± 2 term, so that the dip in the differential
crosssection, mentioned at the end of the previous section, is missing; as
regards to the nonspinflip transitions, both the crosssections that corre
spond to an initial state m = and m = ± 1 show pronounced minima
brought about by the destructive interference of the single and double scat
tering amplitude. The position of these two minima occur at rather dif
ferent values of q since in that range of momentum transfer S 2 (q[2) is nearly
equal to S Q (qf2); thus the single scattering term, in the m = 1 state, which
is weighted by the factor (S — »S 2 ), decreases faster than in the m = state,
where the weight factor is (S \ %S 2 ). As a result in the case of unpo
larized deuterons, the differential crosssection in the interference region is
not very sensitive to the ratio between the real and the imaginary part of
the scattering amplitude; the differential crosssection is instead very sen
sitive to the quadrupole form factor and therefore to the cfwave percentage
included in the wave function of the deuteron.
Coherent scattering of highenergy hadrons
103
10 p
10 3
■4? KV
• 0.895 GeVfc
A 9.0 GeV/t
o 15.2GeV/c
CERN TRIESTE
t (GeV/c) 2
0.5
IjO
1.5
20
2.5
Fig. la.  Differential crosssection for rcd elastic scattering at 0.895, 9.0, and 15.2GeV/c.
The experimental data are from refs. [10] and [12]. The 0.895 curve (•) (ref. [27]) was
computed by using the pionnucleon amplitudes derived from the CERN phaseshift
analysis. For the 15.2 GeV/c curve (o) (ref. [27]) the amplitudes were those of Barger
and Phillips (ref. [21]). In both cases the GartenhausMoravcsik deuteron wave function
was used. For the 9.0 GeV/c curve (a), the scattering amplitude was parametrized as
/fo) = (ifcff/4OT)(l — ia)exp[— 0V/2], with a p = 26.9 mb, a n = 25.3 mb, a p =0.13,
a n = — 0.23, /?* = fil= 8.5 (GeV) 2 ; the Humberston wave function was used for the deuteron.
104
G. Fidecaro and M. Fidecaro
• pd» pd
12.8 GeV/c
preliminary
CERNTRIESTE
a pd»pd
1Q9 GeV/c
Kir ill ova et al
1.0
t(GeV 2 )
Fig. lb.  Differential crosssection for pd elastic scattering at 10.9 GeV/c (a) and
12.8 GeV/c (•). The experimental data are from ref. [1] and [4]. For the nucleon
nucleon scattering amplitude it was assumed that a p = 39.2 mb, a a = 40.2 mb,
a p = « n = 0.33, Pl = fil = 10 (GeV) 2 ; for the deuteron the Humberston
wave function was used.
Coherent scattering of highenergy hadrons 105
In the case of polarized deuterons, if q& is the position of the minimum,
the crosssection at q^ is strongly sensitive to the real part of the hadron
nucleon scattering amplitude at the value q = q&jl and q = q&.
In Fig. 1 we show a sample of data for pions and protons. There is no
dip and the agreement with the theoretical curves is rather good.
The coherent quasielastic scattering can be described in a similar way,
starting from formula (3). The agreement with the experimental data (see
Table IV) is again rather good.
4.  The A>2 case.
A similar analysis has been carried out for He and other light nuclei.
Here the information exists only for protons and is rather limited. The
experimental data for 4 He are compared in Fig. 2 with the curves foreseen
by the model. At low momentum transfer the agreement is good for what
concerns the size and slope of the diffraction peak as well as the size and
position of the first minimum.
The situation changes at larger angles. It seems that a better represen
tation of the data is obtained by decreasing the scattering amplitude with
a change of the nuclear density, in such a way that the term of order n is
decreased less than the term of order (n — 1).
Because, roughly speaking, the multiple scattering amplitude is an ex
pansion in crr^f, where r tj is the distance between two nucleons in the nu
cleus, one can obtain the above effect by increasing the average separation
of the nucleons themselves. This is the case when there are nucleon con
figurations which are preferred or if there is a correlation such that the two
nucleons cannot approach each other beyond a certain limit. In this scheme
Czyz and Lesniak [32] and Bassel and Wilkin [30] have modified the nuclear
density function, given by the independent particle model.
In Fig. 2 the results of Bassel and Wilkin are reported. They tried to
fit the experimental data of ref. [6] either by using a double Gaussian as
density function for the single particle, or by introducing a correlation
function. The fit of these data (as well as of the data for e 4 He elastic scat
tering) is good in the first case (continuous curve of Fig. 2), but not in the
second one (*).
(*) A critical analysis of the kind of interpretation has been made recently by Cro
mer [34].
106
G. Fidecaro and M. Fidecaro
10
10^
>
E10°
D
10"'
10" 2 =
10"
n. '
i i i i i i i i i i i i
1 :
p 4 He
]
"\\
1.7 GeV/c

Palevsky et al.
~
= i\
'
■ v>

\
\
3
: \\\
\
Z
\i
\
\

V

Z
~
\W // \ •*>* ^i. N
*T/. \ ^ s TL x
—
« \ V\\
\ N \ \ s
I
\ \V \


\ VN \ l\
\ w \ i«[ x

~
\ w^h*

E
\ ^ r ^ •
ft
_( 3) 1
\ N * N
■LI

(D\
v
■M :
i
1 1 1 \ 1 1 1 1 1 1
\l
1 •
0.5
1.0
1.5
t (GeV/c)
Fig 2.  Differential crosssection for p 4 He elastic scattering at 1.7 GeV/c.
The experimental data are from ref. [6]. The curves are from ref. [30], and
were computed by assuming for the singleparticle density a Gaussian distri
bution of width R 2 = 1.87 fm 2 ( ), or a double Gaussian distribution ( );
for the nucleonnucleon scattering amplitude it was assumed that a = 44 mb,
a =  0.3 and ^ = 5.4 (GeV/c) 2 (  ), or = 40.4 mb, a =  0.5 and
fP = 54 (GeV)~ 2 ( ). Curve (1) represents the contribution of single scat
tering (impulse approximation), curve (2) single plus double, etc.
The results of a similar analysis for the 4 He data at 1.2 GeV/c [5], and
for 12 C and 16 at 1.7 GeV/c [6], are reported in Figs. 3, 4 and 5.
For the heavier nuclei, A^>1, the scattering amplitude which results
from the sum over the various terms tends to the same form that one would
find by using an optical model of the nucleus; this, in fact, is already true
for the 16 case [35].
Coherent scattering of highenergy hadrons
107
5.  The backward region.
The backward scattering has been studied only in the pd case, and in
a rather limited momentum interval. The important experimental fact is
10
p 4 He
1.2 GeV/c
Boschitz et al.
J I I
I I W I
0.5
t (GeV 2 )
1.0
Fig. 3.  Differential crosssection for p 4 He elastic scattering at 1.2 GeV/c.
The experimental data are from ref. [5]. The curves are from ref. [3>5b] and
were computed by assuming for the singleparticle density a Gaussian distri
bution of width R 2 = 1.56 fm 2 ( — ) or the one obtained from the e 4 He elastic
scattering ( ); for the nucleonnucleon scattering amplitude it was assumed
that a = 39 mb, a = — 0.43 (  ), and a = — 0.5 ( ), £ 2 = 4.3 (GeV/c)" 2 .
108 G. Fidecaro and M. Fidecaro
P 12 C
1.7 GeV/c
Palevsky et al
0.2
t(GeV 2 )
0.3
0.4
Fig. 4.  Differential crosssection for p 12 C elastic scattering at 1.7 GeV/c. The
experimental data are from ref. [6]. The curve is from ref. [356] and was com
puted by assuming for the singleparticle density a Gaussian distribution of
width R 2 = 2.5 fm 2 , as obtained from electron scattering; for the nucleon
nucleon scattering amplitude it was assumed that a = 44 mb, a = — 0.28,
/S 2 = 5.4 (GeV/c) 2 .
the strong enhancement of the crosssection toward the largest angles, as
it is shown in Fig. 6.
In order to extend to the large angles the mechanism that de
scribes forward scattering, let us refer to the pictorial representation of the
Coherent scattering of highenergy hadrons 109
p l6
1.7 GeV/c
Palevsky et al.
n
0.1
Q2
 1 (GeV/c) :
0.3
0.4
Fig. 5.  Differential crosssection for p le O elastic scattering at 1.7GeV/c.
The experimental data are from ref. [6]. The curve is from ref. [356] and was
computed by assuming for the singleparticle density a Gaussian distribution
of width R 2 = 2.92fm 2 ; for the nucleonnucleon scattering amplitude it was
assumed that <r p = 47.5 mb, cr n = 40.0 mb, a = — 0.4, /S 2 = 4.7 (GeV/c) 2 .
Glauber model that is indicated in Fig. 7. If the graphs are interpreted as
Feynman diagrams and certain approximations are made, one obtains the
same values for the crosssection as those obtained from the multiple scat
tering model.
110 G. Fidecaro and M. Fidecaro
10 2 r ■ 1
Pd
Coleman et al.
• 1.7 GeV/c
o 2.0GeV/c
A 2.25GeV/c
1 1.7GeV/c
cms
Fig. 6.  Differential crosssection for pd elastic scattering in the backward
direction at 1.7 (•), 2.0 (o), and 2.25 (a) GeV/c. The experimental data are
from ref. [2]. The curves are from ref. [38] and were computed from the triangle
diagram of Fig. le.
There have been attempts [36, 37] to use this technique for the backward
scattering, but the computed crosssection is an order of magnitude lower
than the experimental data.
An attempt [18] to explain the data on the basis of the exchange diagram
of Fig. le has also been unsuccessful, because the crosssection does not
decrease fast enough when the momentum of the incoming proton is increased.
Coherent scattering of highenergy hadrons
111
a) impulse approximation c) double charge exchange
scattering
P r~\ P P r \ n r\ P
b) elastic double scattering d) inelastic double scattering
e) onenucleon exchange
o
f) triangle graph
Pi ^ d 2
O
^ k(pion)
n D„
Fig. 7.  Graphs describing the pd elastic scattering in the forward (a), b), c), d))
and in the backward (e), /)) direction.
Very recently, Craigie and Wilkin [38] related the protondeuteron back
ward scattering to the case of a pp collision in which a fast deuteron is
produced together with a slow pion; the pion (dashed line in Fig. If) is
afterwards absorbed by the spectator nucleon. The predicted crosssections
are too low, but the angular dependence is in good agreement with the ex
perimental data.
6.  Conclusions.
The experimental results reported in this paper tend to indicate a fairly
good agreement of the experiments with the Glauber model of multiple
scattering. As mentioned in the introduction, this progress has been made
possible by new technical developments. These can still be exploited for
more refined measurements in the forward scattering region and for new
112 G. Fidecaro and M. Fidecaro
measurements at larger angles, including the backward scattering region.
In particular, it seems to be of great interest to perform experiments of this
kind on polarized deuterons, as one could check the model in detail through
simplified experimental conditions. Unfortunately the technique of polarized
targets has not yet reached such a point of refinement.
The success so far obtained does not imply, however, that the theory is
already perfect: much more systematic work of comparison with experi
ments is needed in order to clarify the exact meaning of the various assump
tions and approximations, and to find out the limit of validity of the pre
sent ideas.
REFERENCES
[1] N. Dalkhazhav et ah: Soviet J. Nuclear Phys., 8, 196 (1969).
[2] E. Coleman, R. M. Heinz, O. E. Overseth and D. E. Pellet: Phys. Rev., 164,
1655 (1967).
[3] G. W. Bennet, J. L. Friedes, H. Palevsky, R. J. Sutter, G. J. Igo, W. D. Simpson,
G. C. Phillips, R. L. Stearns and D. M. Corley: Phys. Rev. Lett., 19, 387 (1967).
[4] F. Bradamante, G. Fidecaro, M. Fidecaro, M. Giorgi, P. Palazzi, A. Penzo,
L. Piemontese, F. Sauli, P. Schiavon and A. Vascotto: presented at the Lund
Intern. Conf. Elementary Particles, 25 June  1 July 1969.
[5] E. T. Boschitz, W. K. Roberts, J. S. Vincent, K. Gotow, P. C. Gugelot, C. F.
Perdrissat and L. W. Svenson: Phys. Rev. Lett., 20, 1216 (1968).
[6] H. Palevsky, J. L. Friedes, R. J. Sutter, G. W. Bennet, G. J. Igo, W. D. Simpson,
G. C. Phillips, D. M. Corley, N. S. Wall, R. L. Stearns and B. Gottschalk:
Phys. Rev. Lett., 18, 1200 (1967).
[7] H. C. Hsiung, E. Coleman, B. Roe, D. Sinclair and J. Van der Velde: Phys. Rev.
Lett., 21, 187 (1968).
[8] P. Fleury: Thesis, January 1967 (unpublished).
[9] R. C. Chase, E. Coleman, T. G. Rhoades, M. Fellinger, E. Gutman, R. C. Lamb,
F. C. Peterson and L. S. Schroeder: Phys. Rev. Lett., 22, 1265 (1969).
[10] F. Bradamante, S. Conetti, G. Fidecaro, M. Fidecaro, M. Giorgi, A. Penzo,
L. Piemontese, F. Sauli and P. Schiavon: Phys. Lett., 28 B, 191 (1968).
[11] F. Bradamante, S. Conetti, G. Fidecaro, M. Fidecaro, M. Giorgi, P. Palazzi,
A. Penzo, L. Piemontese, F. Sauli, P. Schiavon and A. Vascotto: Lett. Nuovo
Cimento, 1, 894 (1969).
[12] F. Bradamante, G. Fidecaro, M. Fidecaro, M. Giorgi, P. Palazzi, A. Penzo,
L. Piemontese, F. Sauli, P. Schiavon and A. Vascotto: submitted to the Lund
Internat. Conf. Elementary Particles, 25 June  1 July 1969.
[13] W. Hoogland et al. (Sabre Collaboration): Nucl. Phys., B 11, 309 (1969).
[14] L. M. C. Dutton and H. B. van der Raay: Phys. Rev. Lett., 21, 1416 (1968).
[15a] G. Bellettini, G. Cocconi, A. N. Diddens, E. Lillethun, G. Matthiae, J. P.
Scanlon and A. M. Wetherell: Phys. Lett., 19, 341 (1965).
[156] G. Bellettini, G. Cocconi, A. N. Diddens, E. Lillethun, G. Matthiae, J. P.
Scanlon and A. M. Wetherell: Nucl. Phys., 79, 609 (1966).
Coherent scattering of highenergy hadrons 113
[16] N. G. Birger et al: Soviet J. Nucl. Phys., 6, 250 (1968).
[17] Yu. D. Bajukov et al: Soviet J. Nucl. Phys., 5, 236 (1967).
[18] Yu. D. Bajukov et al: Soviet J. Nucl. Phys., 8, 199 (1969).
[19] J. Banaigs et al: submitted to the Lund Intern. Conf. Elementary Particles (1969).
[20] See also A. de Shalit: Comments on Nucl. Particle Phys., 3, 88 (1969).
[21] See, for instance, L. Bertocchi: Comptes Rendus, Rencontre de Moriond sur les inter
actions electromagnetiques, 1967. However, in the last year a great effort has been
made to get this information by fitting the available pionnucleon data and through
the sum rules technique, e.g V. Barger and R. J. N. Phillips: Wisconsin preprint,
April 1969.
[22] See, for instance, T. T. Chou and C. N. Yang: Phys. Rev., 170, 1591 (1968).
[23] R. Glauber: Lectures in Theoretical Physics (Wiley, Interscience, New York, 1959),
Vol. 1, p. 315.
[24] R. Glauber and V. Franco: Phys. Rev., 142, 1195 (1968).
[25] L. F. Schiff: Phys. Rev., 176, 1390 (1968).
[26] J. Pumplin: Phys. Rev., 173, 1651 (1968).
[27] G. Alberi and L. Bertocchi: Nuovo Cimento, 63, 285 (1969).
[28] G. Alberi and L. Bertocchi: Nuovo Cimento, 61 A, 203 (1969).
[29] D. R. Harrington: preprint, Rutgers University (1968).
[30] R. H. Bassel and C. Wilkin: Phys. Rev., 174, 1179 (1968).
[31] C. Michael and C. Wilkin: Nucl. Phys., Bll, 99 (1969).
[32] W. Czyz and L. Lesniak: Phys. Lett., 25 B, 319 (1967).
[33] R. Glauber and V. Franco: Phys. Rev. Lett., 22, 370 (1969).
[34] A. H. Cromer: Nucl. Phys., Bll, 152 (1969).
[35a] R. J. Glauber: Proc. Int. Conf. HighEnergy Physics and Nuclear Structure (North
Holland Publ., Amsterdam, 1967).
[356] L. Lesniak and H. Wolek: Nucl. Phys., A 125, 665 (1969).
[36] J. N. Chahoud and G. Russo: Nuovo Cimento, 49 A, 206 (1967).
[37] L. Bertocchi and A. Capella: Nuovo Cimento, 51, 369 (1967).
[38] N. S. Craigie and C. Wilkin: Elastic protondeuteron scattering at large angles (to
be published).
The Determination of the Axial Vector Coupling
for Strangeness Nonchanging Currents.
C. Franzinetti
Istituto di Fisica  Universitd di Torino
G. Stoppini
Istituto di Fisica  Universitd di Pisa
1.  Introduction.
According to our present knowledge, weak interaction processes can be
described using a phenomenological Lagrangian density of the type
(1) & = ^J x j; + h.c.,
V2
where
(2a) J x =j$»+jf> + jp
(26) JP = Wa(1 + 7 5 )Vve
(2c) ffl = i^yxil + y 5 ) W
are the local leptonic currents, associated with the electronic and muonic
field, respectively. The hadronic current J^ has, in general, a more com
plicated structure: Following Cabibbo's theory, the strangeness conserving
and strangeness nonconserving parts add up to give
(3) /f)(+) = cos0 v Fj+> + cos0 A ^(/> + sin0 v F s ( +> + sin0 A ,4<+> ,
where V, A, are the vector and axial vector parts of the strangeness non
changing currents and V s ^ and A sX the corresponding parts of the strange
ness changing currents. The (+) suffix is a remainder of the fact that the cur
rent is a chargeraising operator (whereas its conjugate J* is a chargelowering
Axialvector coupling 115
operator). Cabibbo's angles VjA have the values [1, 2]
6 y = 0.232 ±0.013
d A = 0.250 ±0.01 8.
G is the universal Fermi constant
(4) G = (1.4350 ± 0.001 1) x 10" 49 erg cm 3 .
The operation indicated by the asterisk is defined by the equation
w) <> jc = Jjc » J 4: = J 4 >
where + indicates Hermitian conjugation. The change of sign of the fourth
component puts this component on the same position as the others with
respect to transformation under charge and Gconjugation operations.
The strangenessconserving vector current V x is supposed to behave like
a « conserved current », i.e., to satisfy
(6) hV* = 0,
whereas the axial vector part is certainly not conserved. According to the
«isotriplet hypothesis » V x , V*, and the isovector part of the electromagnetic
current (l/e)/J' v form the three components of the same isotriplet.
The most general matrix element of ./= V\A between two single nu
cleon states, satisfying the requirements of invariance of the Lagrangian den
sity under proper Lorentz transformation has
(7) V x = iu p (Ayx ± faxr q^ ± / 3 qx) u n exp [— iqx] ,
(8) Ax = z'WpteiWs + gz<*3LrWs + gzqm)u n exp [— iqx] .
The ft and g*'s are (in general complex) functions of the fourmomentum
transfer squared
(9) q 2 = (p p p Q ) 2 .
If the conserved vector current hypothesis is valid, then
(10a) f 3 (q*) = 0.
Moreover, if the isotriplet hypothesis is accepted, then
(106) f x (q*) = F*™iq*)
(10c) f 2 (q*) =  ^^ F**iq*) ,
116 C. Franzinetti and G. Stoppini
where F ± and F 2 are Hofstadter's nucleon form factors normalized to unity
for # 2 >0; ju p and fi n are the anomalous magnetic moments of the proton
and neutron, respectively in units of Bohr magnetons (^ = 3.69); and M
is the nucleon mass M a = M p = M.
Invariance under time reversal operation imposes
whereas charge symmetry requires
gi = g*, g2 = —gt, g 3 = —g$
Thus g x is real ; g 2 = 0, and g 3 pure imaginary. At variance with the
corresponding form factors of the vector part, the g's are not normalized to
unity when q 2 +0. Putting
G v = Gcos6 w , G A = Gicosd A , G p = G°cos0 p ,
lim gl (q*) = GJG y , lim gjq*) = i(G p /G w ) ,
the entire matrix element for J^ reads
(11) <p/ h )n> = i^m [Fiyx^FiOM +
«(n) exp [— iqx] ,
c c
^F A y x y 5 + i^
+ ^ F A.nYs + i^FpWs
where
*i(0) = F A (0) = 1 .
2.  The determination of G A in experiments at low momentum transfer.
In the limit of low q% the matrix elements (11) reduces to
(12) <pMn> = /j «p Ya(G y + G A y 5 )u n .
Equation (12) can be used to predict the values of relevant parameters and
distributions accessible to experimental determination. From the total decay
rate of the neutron, one deduces
(13) [iG v  2 + !G A  2 P = (1.63 ± 0.02) x 10 4 » erg cm 3 ,
Axialvector coupling 117
G w can be deduced independently from a pure Fermi > transition.
On the basis of seven transitions [3] ( 14 0, 26 A1, M C1, 42 Sc, 46 V, 50 Mn and 54 Co),
the value of G w = (1.4149 ± 0.0022) x 10" 49 erg cm 3 was obtained. Thus
(14) GJG N = 1.18 ±0.02.
This is the best determination of GJG N for strangeness nonchanging
currents. All other experiments, though not as precise, have given results
consistent with eq. (14) (*).
3.  The physical interpretation of the experimental result GJG y = 1.18.
The physical interpretation of this result received a first contribution when
Goldberger and Treiman discovered that
(15)
G v ~ M '
where g n xx is the renormalized pion nucleon constant and f„ the pion decay
constant.
Their deduction was based on complex arguments of dispersion theory:
however it was later rederived starting from different assumptions and using
simpler methods [4].
Let the pion field be defined by the equation
(16) d x A x = c n <p n ,
c r , being a constant (**). The matrix elements of (16) between two nucleon
states is
(17) <pMai» = *W[2MG A F A (<? 2 ) + q 2 G p F p (q*)]u p y 5 u n ,
N being a normalization coefficient. For q 2 >■ this reduces to
(18) <pM» = iN2MG A u p y 5 u a .
We must now calculate the matrix element of the pion field between the
(*) For a complete discussion on this subject see ref. [3] and T. D. Lee and C. S. Wu:
Ann. Rev. Nucl. Sci., 15, 381 (1965).
(**) We omit here isospin indices which are not essential.
118 C. Franzinetti and G. Stoppini
same states. Using the field equation
(19) (P2»ft<P n (x) = J w (x)
we obtain
(20) <pk(0)n> =  jL_ <p jW(0)n> =
D(q 2 )
= ~ a 2 _L m 2 A/2 ftrj^P ^W p y 5 « n ,
where q^ is the pion momentum and D{q 2 ) is, by hypothesis, a slowly varying
function of q 2 in the interval 0># 2 > — ra 2 and accounts both for the re
normalization of the free propagator and the free vertex. The \/2 factor
arises from the isospin pionnucleon coupling. Then D(q 2 ) is intended to be
normalized to 1 for q 2 = — m 2 , i.e.
Z)(— /w 2 ) = l.
At # 2 =0 we hawe, using (16),
2MG A = V2^fD(0)c n .
mi
We can deduce c n from the measured 7>decay rate. This is in fact deter
mined by the matrix element
<0i4j7U> = I^^ a <0^7U>
and one obtains
c n = y/2f n m% ,
where f n is the (experimental) decay constant of the pion (y/2f n ^
~133MeVxG v [5]).
Thus
(21) G A = ^™^ G v D(0) .
If D(q 2 ) does not change appreciably moving from q 2 = — m 2 to q 2 — 0,
then (21) coincides with (15). Putting the measured values of the constants
in (15), one obtains
GJG W ~1A.
Axialvector coupling 119
The difference between this value and the experimental one (eq. (14))
is ■ — 15%. The origin of such difference may well be due to the (q 2 = — m 2 ^
_> q* = 0) extrapolation of the form factor D(q 2 ) (see GellMann and Levy [4]).
The hypothesis formulated in eq. (16) is often referred to as Partially
Conserved AxialVector Current hypothesis (PC AC). It may be expressed
in a different way, namely by stating that the matrix elements of the diver
gence of the axialvector current satisfy unsubtracted dispersion relations and
that the immaginary part of this amplitude is essentially determined by the
onepion pole at q 2 = — m^.. Thus, although no extrapolation of the form
factor is involved here the result is not exact because of the somewhat arbi
trary neglect of the background contribution beginning at q 2 =— m 2 .
A major step toward our understanding of the origin of the renormaliza
tion of the axial vector coupling was made independently by Adler [5] and
by Weisberger [6].
Adler's deduction which is based on a method proposed by Fubini and
Furlan [7], starts from the following assumptions:
a) That the pion field is defined by the equations
SttJVJV 1 °V
« i » being an isotopic spin index and C% an isospin ClebschGordan coefficient.
b) That the fourth components of the axialvector currents satisfy
GellMann's equaltime commutation relations
(23) [A\{x\ Ai(y)] x ^ Jt =  d(x y )e m V*(x)
and obtains the following equation relating G V /G A to the offmassshell pion
nucleon crosssections :
/G v \ 2 2M 2 1 f dW 2 . . , , . , X1
(24) ' " (si) = ^ n) m=m ['°v* + p)— » ff (*p)] .
The numerical evaluation of (24) requires some care since the offmass
shell crosssections are not the experimental ones. He carries out the extra
polation assuming that the 33 /?wave resonance predominates and obtains
GJG y = 1.24.
Weisberger, using a different formulation which does not imply offmassshell
extrapolations (nor the Goldberger and Treiman relation) obtains
G A /G V =1.15
120 C. Franzinetti and G. Stoppini
in excellent agreement with the experimental value (14). Other methods to
obtain (24) have been indicated (Adler [5], Weisberger [6] Fubini and
Furlan [7]) which the reader may find in the literature quoted here.
It is interesting, in this connection to mention that Weinberg [8] has
obtained a sum rule which differs from (24) only in terms of the order 0(m 2 fM^,)
starting from the GoldbergerMyizawaOehme sum rule for the pionnucleon
scattering lengths a%— a%. Turning the other way around one deduces a
relation between aj — a% and GJG y .
4.  The # 2 dependence of the axialvector coupling.
4*1. Neutrino experiments.  The most direct way of investigating the
dependence of the axialvector coupling on q 2 is the study of elastic reactions
produced by energetic neutrinos, i.e., processes of the type
(25) v t +n>r+p
(26) v t +p^t + +n,
where t is a lepton and vt the neutrino associated with the corresponding
lepton field.
The theoretical distribution da/dq 2 =f(E Vi q 2 ), ZT V being the primary neu
trino energy, can be deduced from eq. (11). Neglecting terms proportional
to the lepton mass, one obtains
(27) (S); = S S* k [A(q2) ± xB ^ + x * c « ] '
the ± sign before B(q 2 ) referring to v and v reactions, respectively. Moreover,
putting A/x = ^ p — /^ = 3.7 B.N.M.
A = 4MV (^J (F 2  F 2 ) + q 2 [fj + 4£^F x F t + F 2 ty + (^V^l
(28) iB^F^ + ApF^q 2
Experiments to measure the functions A(q 2 ), B(q 2 ), C(q 2 ), and hence F A (q 2 )
have been performed at CERN and Argonne National Laboratory, using
Axialvector coupling 121
spark chambers and heavy liquid bubble chambers. The analysis was
carried out assuming F 1 and F 2 were identical with the electromagnetic form
factors; and F A (q 2 ) was represented by the parametric form
(29) F A (q 2 )
(•+&
with M A to be determined from fitting the experimental data. The results are:
a) at CERN:
Spark chamber exp. [19] M A = 0.65±£ff GeV/c 2
Bubble chamber:
(freon filled) [10] 0.9±g;f GeV/c 2
(propane) [11] 0.7±0.2 GeV/c 2
b) at Argonne National Laboratory:
Spark chamber exp. [12] 1.05±0.2 GeV/c 2 .
The errors quoted here are largely due to nuclear effects which make
it difficult both to select genuine elastic events and also to determine precisely
the relevant kinematical parameters. In fact, reaction (25) takes place on
neutron target, namely inside nuclei. Also using propane, i.e., carbon targets
which are comparatively small nuclei, nuclear effects such as scattering of
protons, Fermi motion, pion absorption, cannot be neglected. The size of
such effects has been estimated using simple models by Montecarlo meth
ods [13] and also by more sophisticated nuclear models [14]. Two typical
experimental distributions of dajdq 2 (integrated over the neutrino spectrum)
are shown in Fig. 1, 2 and 3.
If the crosssections dafdq 2 is measured for processes (26) as well, the
axial form factor can be directly computed.
In fact, from (27) and (28)
< 30 > (SI." (a?L = ^ w, (4M£ '" ™ + A "^ 2 > •
Experiments with antineutrinos have been attempted but, so far, have
not yielded substantial results. In fact it is much more difficult to produce
a clean beam due to the unfavorable ratio tz~/k + in meson production processes
by protons. Moreover, the process (26) produces only one charged particle
in the final state, i.e. a [i + or an e+. No kinematical fit can be made to
establish the nature of the event which has to be assumed a priori.
A less direct way of measuring F A {q 2 ) is given by the neutrino inelastic
events
(31) vjJf >r+jr+7r,
122
C. Franzinetti and G. Stoppini
q 2 CGeV/c) 2
Fig. 1.  The q 2 distribution of neutrino events observed in the CERN freon
filled heavy liquid bubble chamber (HLBC). The different curves refer to
different axialvector form factor assumed [11].
where JSP, JV" indicate a nucleon, either a proton or a neutron. The hadronic
current is, in this case, given by a much more complicated expression than (1 1).
It can be seen that the most general matrix element is formed by 8 vectors
and 8 pseudo vectors. Conservation of the vector current reduces the number
of terms from 16 to 14 and the « isotriplet vector current hypothesis » deter
mines the vector current directly from electro and photoproduction data.
The axialvector part can be calculated with the help of dispersion relation
technique. Let Mi be the projection of the axialvector amplitude on the
Axialvector coupling
123
20"
Experimenhal values
rr conlTibuMon
to
c
>
<D
O
d
10
TheoreMcal curve
for M A = 0.7GeV/c 2
0.2 0.4 0.6
0*8
1.0
q 2 CGeV/c)
Fig. 2.  The q 2 distribution of neutrino events observed in the CERN propane
filled HLBC. The open circles (o) indicate the estimate contribution to the
background of nonelastic events of the type v+n > [I'+p+iz . The filled cir
cles (•) indicate the experimental values.
/th multipole and let us assume that Mi satisfies the dispersion relation
(32)
Mi(W) = Mf +
7tJ
Im Mj(W)dW r
W'—W
where Mf is the contribution of the Born terms to the same multipole.
The solution of eq. (32) is proportional to Mf and thus is a linear function
of F A (q 2 ). Thus (*) an analysis of « single pion » events gives in the end an
estimate of F A (q 2 ).
This analysis is much more elaborate and perhaps less valid than that
on the elastic events, due to the various assumptions and approximations
(*) The induced pseudoscalar term, which is proportional to the lepton mass, does
not contribute appreciably to the axial vector matrix element.
124
C. Franzinetti and G. Stoppini
a
a>
o
o
50
40
elastic events
+ inelastic bkg.
M A = 0.84GeVl e(ashc
M A =0.5 GeVjevents
1.2 14 CGeV/cV
Fig. 3.  The q 2 distributions of neutrino events observed in the CERN spark
chamber [9] and selected according to the criterion: E v ~ 1.4 GeV; cos cp en 0.8.
The curves give the theoretical distributions estimated for the elastic events +
+ inelastic background for different values of M A .
which are involved in the calculations. However, if it is assumed to be valid
and the theoretical curves thus obtained are fitted on the experimental distri
butions, one obtains (assuming F A (q 2 ) to be as in eq. (29)):
a) experiment using the C 3 H 9 filled bubble chamber:
for the reactions v+p ^(jt+^ + +P, M A = 1.250±0.350 GeV/c 2
for the reactions v+J^>[x+7u +JV", M A = 0.850±0.250 GeV/c 2
b) experiment using the freonfilled bubble chamber
for the reaction v+ JV > {x~+ tt + JY", M A = 0.900±0.250 GeV/c 2 ,
where JV or JV" indicate a nucleon, either a proton or a neutron. Thus within
these large limits of uncertainty it appears that the « axialvector radius »
of the nucleon does not differ appreciably from the vector form factor.
Theoretical predictions on the form of F A {q 2 ) are rather vague at present.
Sum rules, connecting the nucleon form factors (and hence F A {q 2 )) to the
inelastic structure factors have been obtained by Adler [5]. « Structure fac
tors » are the quantities oc(q 2 , W), ft(q 2 , W), y(q 2 , W) in the expression of the
crosssection
& 2 o
dQ t d£ t
(v+^ > C+H) = G ( ^f ° Ei [g 2 a + 2£ v £ t cos 2 1 fi 
■(Z, + Et)q*y\
Axialvector coupling 125
where t indicates a lepton, q 2 = Q? v — pt) 2 , £ v the neutrino energy, and <p
the angle of emission of the charged lepton with respect to the neutrino;
W is the mass of the final hadronic system H, 6c=0 A f^6 w . However a, /?, y
are far less known than F A (q 2 ) and also less easy to be determined over a
wide range of q 2 and W. Thus these rules — which are in fact tests of local
commutation relations — are in general of little help to determine the axial
vector coupling.
4"2. Lowenergy single pion electroproduction.  Symmetry considerations
involving weak and electromagnetic interactions, suggest the existence of
similarities between process (31) and the process
(33) e+J^e+JV'lTr,
so that one has to expect to be possible to express the amplitudes for both
processes in term of common form factors, namely the vector and axial vector
form factors.
Under the hypothesis of a single photon exchange between the electron
and the hadronic system, process (33) is equivalent to a single pion photo
production process induced by an offmassshell photon so that one has to
expect the existence of both transverse and longitudinal amplitudes [15].
Furthermore, for given initial and final electron fourmomenta, the e.m.
radiation possesses a welldefined polarization state described by the polariza
tion parameter
l
(34)
l+2^ 2 tg^'
^ k 2 8 2
which measures the transverse linear polarization of the virtual photon.
Here k^ is the photon fourmomentum and \p the laboratory electron scat
tering angle.
The differential crosssection for scattering into the electron solid angle
dQ% measured in the laboratory and into the pion solid angle dQ„ measured
in the 7>JV cm., is given by
(35) d ' tf  * E '\ k \\\ jTVi^
y } dE'dQidQ K 2n 2 Ekl y ' dQ n '
where E, E' are the initial, final laboratory electron energies; \k\, k are the
laboratory photon 3momentum and energy (k = E — E'); daJdQ^ is the
7CJNP cm. differential crosssection for pion production by a virtual photon
126 C. Franzinetti and G. Stoppini
and can be written as
( 36 ) U^ = ^t + ^l^l + 5cos2?> + Ccos9?,
where \q\ is the pion 3momentum ; <p is the angle between the planes of
initial and final electrons and initial electron and final pion; <£l = (k z jkfy£ > .
The first term represents the crosssection for pion production by an
unpolarized, transverse virtual photon; the second term is the crosssection
for pion production by a longitudinal photon; the third term arises from
the interference between transverse states while the fourth from interference
between longitudinal and transverse states.
That is all can be inferred by the hypothesis of a single photon exchange
and by the use of the properties of the electromagnetic field. An evaluation
of the At, A l , B, C coefficients implies dynamical considerations on the in
teraction of the e.m. field with the hadronic system and we have to expect,
on general grounds, that they will depend on k 2 , q 2 , and 6 n (the 7uJ\P cm.
angle between photon and pion). If eq. (35) is integrated over the 6 and <p
variables one obtains
(37) afe = £• §' 13 (1 " gyl M * 2 ' w) + '"**> w)] •
where
o o
j1 or T = n \A T d(cos 0„) , j^. er L = 2n \A L d(cos &„) ,
1^1 J \9\ J
W = \/ml + ? 2 + VM 2 + ^ 2 ,
and or, a^ measure the total absorption crosssection for transverse and,
respectively, longitudinal virtual photons. In the following (37) will be referred
as « total crosssection ».
By using the PCAC and current algebra hypotheses, it is possible to
obtain definite predictions on the single pion electroproduction amplitude for
the pion fourmomentum q^^O. Under this condition, that for external
pions implies w Jt >0, Adler and Gilman [16] and Riazuddin and Lee [17],
have been able to obtain sum rules through the comparison of a standard
dispersion calculation with the PCACcurrent algebra approach.
In general, an evaluation of a zero pion mass amplitude runs through the
following steps [8]:
Axialvector coupling 127
a) An offmassshell amplitude is defined and by using the PCAC
hypothesis a reduction formula is obtained as a sum of two terms: for pro
cess (33) one term contains the fourthcomponent of the axial currentvector
current commutator (equaltime commutator) and the other contains the
axial currentvector current timeordered product.
b) Current algebra commutators can then be used to obtain the term
due to the equaltime commutator while, when q^ » 0, in the timeordered
product, only the single nucleon pole survives to which continuum contribu
tions beginning at q 2 = — 9m 2 . have to be added. For elastic izJf scattering,
for instance, in the ^complex plane, the single nucleon pole is at Re q =
= — m\l2M while the threshold unitarity cut starts at Re q = m n . When
m n > both the single nucleon pole and the threshold go toward q =
so that one can expect that the amplitudes evaluated for q n > (including
only the singlenucleon pole contribution) represent a good approximation
to the low energy physical amplitudes. It has to be noticed that the pole
terms obtained in the limit q n ^0 do not contain the pion pole.
c) An estimate of the low energy amplitude on the mass shell is then
performed extrapolating from the zeropionmass expression.
The first step, as a definition, implies a certain amount of arbitrariness.
The problem of the extrapolation of the zeropionmass result to physical
pions is not trivial and the procedure to solve it is not unique. In general,
the used procedures are all based on the assumption that the offmassshell
amplitude is a smooth function of q as would be expected in a perturbation
expansion, based on a Lagrangian field theory for which the PCAC hypothesis
holds.
We quote here two extrapolation methods which allow to obtain def
inite predictions for process (33):
Method I. Balachandran et al. [18], following a proposal of Sugawara [19]
and Suzuki [20], obtain local statements about physical quantities from cur
rent algebra and are able to approximate the physical amplitude in terms
of the value of the offmassshell amplitude and its derivatives evaluated at
an appropriate unphysical point.
Method II. To perform the extrapolation to physical pions, Fubini and
Furlan [21] propose the use of mass dispersion relations and give definite
prescriptions on the path along which it is convenient to extrapolate, namely
a path along which the amplitudes are almost constant. The FubiniFurlan
method gives predictions for physical amplitudes in defined points of the
physical region: for process (33) this is done at the nucleon Breitthreshold.
Method I predicts the pionnucleon scattering length with a precision
128
C. Franzinetti and G. Stoppini
of ~ 10 %. Method II predicts the same physical magnitudes with a precision
of 10 to 20 %, while applied to threshold single pion photoproduction predicts
the 71+ threshold matrix element to better than 10% and remarkably well
the threshold tz~/'k + ratio.
Method I has been used by Gleeson et al. [22] to evaluate the positive
pion electroproduction amplitude at the physical threshold. At the physical
threshold, we have
w
l\9\
T TT+n
7 T
r 7T+n
«0
«0
= \E&*(k\q = 0)\ 2
= \Lt + \k\q = Q»\\
£o+, L 0+ being the transverse and longitudinal electric dipole J =\ transition
amplitudes.
The Gleeson et al. predictions are
Ef + \k\ q = 0) = V2& [" n GXiW^F^)  F A (k*)] ( 1 + ^ J
m\k\ q = 0) = <flQ \ l + 4tfi G"p/0
where
([
k*
G?(k*)^F^
i(* 2 )(
+
Ai^)2F A (^)
k 2 \
kF x {k 2 ) = F\(k 2 ) — Fl{k 2 )
Q _k^ V 2 (4M 2 + A: 2 )*
~c2M gA 2M 2 + k 2
G\{k 2 ) = Fl{k 2 )
4M'
F$(k 2 )
and c is denned through the PCAC relation d^A* = ^/2~\c + \(p+. The authors
claim that, within the method, the amplitudes are correct to better than 15 %.
Method II has been used by Furlan et al. [23] to evaluate the single tt + elec
troproduction amplitude at the nucleon Breitthreshold. For & 2 < 10 4 fm
the \q\ values corresponding to the nucleon Breitthreshold range from ~ 10
to ~ 35 MeV/c so this prediction can be easily used, by only introducing
kinematical factors, to evaluate the physical threshold amplitude. Their
result depends on F A and F , but using the relation between them given by
Axialvector coupling 129
the pion pole dominance hypothesis it can be written as
E ^ k2 >« = °^w{k
\Fa(<) + ^G%\t)G A (0)
+ <5
where F A (t) is the axial vector form factor of the nucleon; G M {t) — F^ + F%
is the Sachs nucleon form factor; t = k 2 — m\ — 2m n k is the nucleon four
momentum transfer at threshold; d and y are corrections to the main soft
pion term and the authors are able to give a precise recipe to evaluate them.
Both the above formulas, at the limit A: 2 »0, reproduce the features
of the KrollRudermann theorem.
For the reaction e+p^7r + +nf e, Amaldi et al. [24] have recently pub
lished an experimental result of the threshold amplitude at k 2 = 5frrr 2 . The
experiment was a measurement of total crosssections in the interval of \q\
from 30 to 80 MeV/c. The experimental apparatus is shown in Fig. 4. It
consists of an electron magnetic channel through which k 2 and q are deter
mined for fixed incident energy. By detecting the coincidences of electrons
with the protons of the concomitant processes
/ T + e +P
e+P x
x 7i°fe+p
it is possible to evaluate what fraction of the single electron arm rate is attri
butable to process (33). As a result of this subtraction method, the authors
obtain the data of Fig. 5 already corrected for radiative corrections. By fitting
the data with a fourthorder \q\ polinomial, the authors obtain, at 5fm 2
lim Iri JTTX^l = ( 4  9 ± ° 7 ) x 10 ~ 31 JflL, ,
«*o [\q\ dQidE'] sr(GeV) 2 /c
which is proportional to \Efc n (k 2 , \q\ = 0) 2 +<^ L Ls; n (& 2 , \q\ =0) 2 . A com
parison of this experimental result with the Gleeson et al. predictions where
use is made of the axial form factor parametric representation
A: 2 \ 2
0+5)
gives
M A = (1.03 ± 0.07) GeV.
130 C. Franzinetti and G. Stoppini
4 PROTON TELESCOPE
ELECTRON MAGNETIC
CHANNEL
^frA '
1m
HZHE 2
Fig. 4.  Experimental setup for tt+ electroproduction total crosssection meas
urements: channel 2 of proton telescope detects mainly tt° protons while chan
nel 1 detects wideangle bremsstrahlung protons.
The fit made by using the Furlan et al. amplitude gives a similar value
of M A .
To decide the most appropriate extrapolation procedure, a comparison
of the predictions with the threshold electroproduction amplitude is more
efficient than with low energy pionnucleon scattering and threshold single
pion photoproduction. As a matter of fact, the electroproduction physical
threshold amplitude is a function of the virtual photon mass and a more
complete experimental investigation of the threshold region could indicate
the best representation of the amplitude and, in the mean time, give an
efficient way to measure F A (k 2 ). The extension of the results to a range
of k 2 is now in progress by using an electronneutron coincidence method.
Axialvector coupling
131
<G">
m
20
15"
OJ
E
u
OJ
10
e+p».e+n+TT +
• E = 800MeV
o E = 780 MeV
0.2
04
0.6
0.8
Fig. 5.  Experimental results on tc+ electroproduction (e+p > e+n+^+) near
threshold referring to two different settings of the primary electron energy.
(•): E= 800 MeV; (o): E = 780 MeV.
Furthermore, it would be useful to allow a still more detailed comparison
with the predictions, obtaining separate experimental informations on the
threshold transverse and longitudinal amplitudes. This could be accom
plished by performing measurements, at the same k 2 value, for different
values of $ but unfortunately this method encounters serious counting rate
difficulties. Another method could consist in measuring the cm. angular
distributions of pions for low values of \q\. In fact, for fixed k 2 , \q\ and
d n , the <f> distributions gives A = At + ^l^l, B, and C separately. Limit
ing ourselves to s and p waves we obtain for A, B, and C expressions of
the type
tf~M = A + A x cos 6 n + A 2 cos 2 B n
Iql^B = smd n (B + B lC osd n )
I^C^Cosin 2 ^,
where A , ... are only functions of k 2 and \q\ 2 . At threshold only A is dif
ferent from zero. Of the other coefficients can be measured the slopes at
132 C. Franzinetti and G. Stoppini
threshold. Having obtained these experimental informations, one can see by
using a multipole expansion that it is possible, within reasonable hypotheses,
to separate the threshold longitudinal and transverse amplitudes. An exper
iment is now in progress at NINA (Daresbury) to measure low energy an
gular distributions of the pion.
REFERENCES
[1] N. Brene, L. Veje, M. Roos and C. Gronstron: Phys. Rev., 149, 1288 (1966).
[2] F. Eisele, R. Engelmann, H. Filthuth, W. Fohlisch, V. Hepp, E. Leitner, W. Pres
ser, H. Schneider and G. Zech: Z. Phys., to be published.
[3] C. S. Wu and S. A. Moszkowski: Beta decay (Wiley Interscience, New York 1966).
[4] Y. Nambu: Phys. Rev. Lett., 4, 380 (1960); M. GellMann and M. Levy: Nuovo
Cimento, 16, 705 (1960); J. Bernstein, S. Fubini, M. GellMann and W. Thirring:
Nuovo Cimento, 17, 757 (1960).
[5] S. L. Adler: Phys. Rev., 140, B 736 (1965).
[6] W. I. Weisberger: Phys. Rev., 143, 1302 (1966).
[7] S. Fubini and G. Furlan: Physics, 1, 229 (1965).
[8] S. Weinberg: Phys. Rev. Lett., 17, 616 (1966).
[9] M. Holder: Thesis Aachen Interner Bericht, 19 (1967); M. Holder, A. Stande,
A. Bohm, H. Faissner, H. J. Steiner, J. K. Bienlein, G. von Dardel, F. Ferrero,
J. M. Gaillard, H. J. Gerber, V. Kaftanov, F. Krienen, C. Manfredotti, M. Rein
harz and R. A. Salmeron: Nuovo Cimento, 57 A, 338 (1968).
[10] C. Franzinetti and E. Young: CERN, NPA/Int. 6619.
[11] Yu. Budagov, D. C. Cundy, C. Franzinetti, W. B. Fretter, H. W. K. Hopkins,
C. Manfredotti, G. Myatt, F. A. Mezrick, M. Nikolic, T. B. Novey, R. B. Pal
mer, J. B. M. Pattison, D. H. Perkins, C. A. Ramm, B. Roe, R. Stump, W. Venus,
H. W. Wachsmuth and H. Yoshiki: in press.
[12] R. L. Kuston, D. E. Lundquist, J. B. Novey, A. Yokosawa and F. Chilton: Phys.
Rev. Lett., 22, 1014 (1969).
[13] C. Franzinetti and C. Manfredotti: CERN NPA/Int. 6730.
[14] A. OrkinLeconrtois and C. A. Piketty: Nuovo Cimento, 50 A, 927 (1967).
[15] N. Dombey: Rev. Mod. Phys., 41, 236 (1969).
[16] S. L. Adler and F. J. Gilman: Phys. Rev., 152, 1460 (1966).
[17] Riazuddin and B. W. Lee: Phys. Rev., 146, 1202 (1966).
[18] A. P. Balachandran, M. G. Gundzik and F. Nicodemi: Lectures on Theor. Phys.,
9B, 361 (1967).
[19] H. Sugawara: Phys. Rev. Lett., 15, 870 (1965).
[20] M. Suzuki: Phys. Rev. Lett., 15, 986 (1965).
[21] S. Fubini and G. Furlan: Ann. Phys., 48, 322 (1968).
[22] A. M. Gleeson, M. G. Gundzik and J. C. Kuriyan: Phys. Rev., 173, 1708 (1968).
[23] G. Furlan, N. Paver and C. Verzegnassi: Nuovo Cimento, 62 A, 519 (1969).
[24] E. Amaldi, M. Balla, B. Borgia, G. V. Di Giorgio, A. Giazotto, P. Pistilli,
S. Serbassi and G. Stoppini: to be published on Nuovo Cimento.
Old Problems and New Ideas
in Elementary Particle Physics.
S. FUBINI
Istituto di Fisica  Universitd di Torino
After twenty years of elementary particle physics we are still very far
from having a satisfactory theory accounting for the different phenomena in
this field.
Although one might feel that this situation is somewhat justified by our
experimental knowledge of the spectrum and of the interactions of elementary
particles, I think that the main reason is indeed theoretical.
In our field we are dealing with an extremely relativistic problem, where
the binding energies are of the same order of the masses, so that creation and
destruction of particles is the most usual phenomenon. This has not as yet
allowed us (and probably never will) to isolate from the general structure
some less complicated system for which to construct a simple selfconsistent
theory.
As an example we can consider a twobody process:
(I) A+B>C+D.
The relativistic nature of the problem requires that the same amplitude
represents at the same time the « crossed» processes
(II) A+C^B+D
and
(HI) A+D>B+C,
where A, B, C, D, are the antiparticles of A, B, C and D.
We denote by Pa, Pb, Pc, Pd the four momenta of the particles and define
134 S. Fubini
the invariant quantities:
(1)
s =(pa + Pb) 2
t = (Pa—Pc) 2
u = (pa—Pd) 2
which represent the square of the cm. energies in channels (1), (II), and (III),
respectively.
We recall the kinematical relation
(2)
s + t + u = 2 M\
The situation can be thus represented by the triangular plot of Fig. 1,
in which s, t and u are represented by the distance of our point from the
s, t and u axes.
In the case of equal masses the three physical regions for processes (I),
(II) and (III) are represented by the crosshatched regions in the plot. Those
regions are indeed disconnected. Since we are dealing with analytic functions
U t
Fig. 1.  See text for explanation of symbols.
Old problems and new ideas in elementary particle physics 135
of s, t, and u, continuation between one physical region and another is possible
One of the fundamental problems in elementary particle physics is to con
struct a scattering amplitude which can be analytically continued from one
region to the other and satisfies all fundamental physical constraints (like
unitarity) in all regions.
The triangular plot in Fig. 1 provides us with a simple way of recognizing
how much of relativistic dynamics is present in one problem. This is achieved
by comparing the size of the fundamental (s, t, u) triangle with some char
acteristic energy of the problem, for example the average distance (or better
Ml— Ml) between energy levels.
In questions of low energy nuclear physics the size of the triangle is of
the order of the square of the mass of the nucleus, whereas the average level
spacing is of the order of mega electronvolt. In this case one can live
happily without worrying about the existence of crossed channels. On the
other extreme, for pionpion scattering, the size of the triangle (~4m%) is
of the same order (and even smaller) as compared to m* — m\ . We thus
face the much more difficult problem of providing an amplitude which is
simultaneously « reasonable » in all three channels.
In particular, if we want to discuss a model in which the main effect is
due to the exchange of resonant states in all channels we have to look for a
crossing invariant generalization of the BreitWigner formula.
During the last few years a new point of view has been developed in this
respect. This has led to the socalled « duality principle » which (in the case
of twobody collisions) requires that the sum of all resonant contributions in
the s channel does automatically represent the sum of contributions to the
crossed t channel.
A simple, beautiful realization of duality is given by the Veneziano rep
resentation in which the twobody scattering amplitude has the form
(3) A(s, t, u) = Ax(s, t) + Au(t, u) + A m (w, s) ,
where
i
(4) Afat) = fx*<«>i (1  x)«(0id;c
o
and analogous expressions for An and Am.
The exponent oc(s) appearing in eq. (4) is a linear Regge trajectory
(5) x(s) = as + b .
136 S. Fubini
Each integer intercept oc(s) = n corresponds to the mass of one (or more!)
resonance. Equation (5) represents the case in which all resonances are taken
in the limit of zero width.
Let us go back to eq. (4); substituting x= \—y we obtain for A\(s,i)
the reciprocal form:
(6)
Aifo = f(l — y)«(s)ly«(t)l dy #
If we now expand the term (1 — x) < *^ )1 (in eq. (4)) and in powers
of x we obtain:
(7) A I (s,t) = 2 Cnit)
o oc(s) — n
Ai(s, t) is thus written as an infinite sum on s channel resonances.
On the other hand, if we expand the term (1 — _y)*(*)i (in eq. (6)) in
powers of y, we obtain for Ai(s) the completely equivalent form
(8) A,(M) = 1 C * (5)
Va(0 — n
as an infinite sum of t channel resonances.
Besides the perfect duality property exhibited in eqs. (7) and (8) the Vene
ziano formula has many appealing features. The asymptotic behaviour follows
the Regge law in all three channels; moreover all constraints due to super
convergence and finite energy sum rules are automatically satisfied.
A recent wonderful development has been the generalization of the ex
pression for the twobody amplitude to processes with any number of external
lines. Those amplitudes do again satisfy duality (which is now a much more
stringent requirement because of the larger number of crossed channels)
and exhibit the wellknown multiRegge behaviour in all channels.
All this might suggest that we are dealing, not only with a beautiful model
for scattering amplitudes but, maybe, with the starting point of a new general
theoretical scheme for elementary particle physics. Time will tell. At present
the weakest point is the absence of unitarity. The resonant dual amplitudes
look very much like generalized Born approximations. Until now, attempts
of introducing unitarity in a systematic way have met with great difficulties.
Waiting for some new ideas which might get us out of this deadlock;
some interest has been devoted to the more modest question of understanding
the nature of the resonant states appearing in the dual models. It has been
Old problems and new ideas in elementary particle physics 137
found that the different intercepts:
(9) a(s) = n
do not correspond to single resonances, but to very degenerate states. For
large n the degree of degeneracy increases as exp [en], i.e., exp[c'\/5]
It appears that this rapid growth of the number of levels with energy is
needed in order to satisfy all constraints related to duality.
This somewhat unexpected feature of the level structure of dual resonant
models is by no means unreasonable. It tells us that the concept of a single
resonances is a useful one only at sufficiently low energies (in the giga electron
volt range). At larger energies the number of levels for energy intervals
becomes so great that we shall practically have to deal with a continuum in
which the single levels will lose their individuality.
Thus we can use the dual resonant models as starting points of statistical
considerations about average properties of such levels.
Let me close this short survey by an optimistic note. Although the still
unsolved questions look formidable and many years of hard work might
still be needed, I think that the new approach based on duality is a modest
step in the right direction. This may finally lead to a satisfactory theoretical
treatment of strongly interacting elementary particles.
HighEnergy e + e~ Annihilation into Hadrons.
R. Gatto
Istituto di Fisica delVUniversita  Padova
Istituto Nazionale di Fisica Nucleare  Sezione di Padova
1.  In 1961 the Italian Institute for Nuclear Physics, under the Presidency
of Amaldi, took the important decision to start the construction of Adone,
an e+e~ storage ring designed to reach a total energy of 3 GeV. The machine
has recently been successfully operated [1]. In the meantime spectacular
developments in the field have taken place at Novosibirsky and at Orsay [2]
thus encouraging the hope of further interesting experimental results.
Investigation of the theoretical aspects of e + e~ collisions had started
very early in Rome and in Frascati [3, 4], leading to the conclusion that
e + e _ storage rings, when available, would be of foremost importance to
the development of highenergy physics. In the last Section of the paper
in ref. [4], Cabibbo and I discussed two points that have appeared to be of
some interest recently [58] : a) the connection of e+e~ crosssections to hadronic
contributions to vacuum polarization; b) the possible asymptotic behaviours
of the crosssection. In this note I shall further develop such points essen
tially with the aims to provide a classification of crosssection behaviours
and related sum rules, and to illustrate the possible underlying physical
interpretation. In relation to the latter point we shall find interesting con
nections to the concept of compound field algebra (CFA). CFA has appeared
of interest in an investigation of leading divergences in weak interactions
relevant to a theory of the Cabibbo angle [9].
Using the YangMills theory [10] and the developments by Lee, Weinberg
and Zumino [11] to provide a frame for the discussion, we shall here sug
gest the classification summarized in Tables I, II and III. We hope that
higher energy colliding beam experiments may bring decisive information in
choosing among the alternatives presented in the Tables.
2.  Here I shall briefly summarize some of the older results by Cabibbo
and myself [4] which are relevant to the present discussion.
Highenergy e + e~ annihilation into hadrons 139
Table I.  Finite field algebra (FFA).
/■
Q(o 2 ) 2 Z
da 2 < oo m n <. oo — >0
Z
\da 2 Q (o 2 )<co g ^ Z>0
4U )f<°°
(^^(?)f i s tne Feynman propagator for the gauge particle.)
Asymptotic behaviour: g 2 q(o 2 ) > 0.
a(s) vanishes more rapidly than s~ 6 (*). (For instance o(s)~s~ 6 (log s)~ 2 , etc.)
e.m. mass differences expected to be infinite (i.e., uncalculable) ; finite Schwinger term in
[j Ji\; finite cnumber term in [8^ — dj ,j k ].
(*) In cm., s = IE.
We assumed that the analysis could be reasonably limited to lowest
electromagnetic order, at least for a finite range of energies. One calls F a
set of hadronic final states produced according to
(1) e++e^F
and gf(E) the crosssection for such a process at energy E of e+ in cm. (total
energy in center of mass = 2E). The set F will contribute a term n F (K 2 )
to the absorptive part, n(K 2 ), of the photon propagator. Here K 2 is the
virtual photon momentum
(2) K 2 = — 4E 2 .
It was stressed in ref. [4] that, for any set of final states F, n F and of are
related through
(3) a F {E) = ~n F {4E 2 )
and that the existence of such a relation was indeed one of the most inter
esting aspects of the theory of e 4 e~ annihilation. Relation (3) is equivalent
to the relation
(4) q f (4E 2 ) = ^ 2 o f (E),
between a F {E) and the contribution from the set F to the spectral function
140 R. Gat to
Table II.  Divergent field algebra (DFA).
da 2 <oo /w„>oo — >0
o 2 Z n
dCT 2 ^((T 2 ) = oo gl^oo Z>0 (Z ^0)
^(0) F < oo
e(ff 2 )^o
0(i) vanishes more rapidly than 5 4 (for instance o(s) ~ 5 4 (log s)~ 2 , etc.).
e.m. mass differences infinite; finite Schwinger term in [j , y'J; infinite cnumber term in
^(cr 2 ) which appears in the LehmanKallen representation [12] for the vacuum
expectation value of the e.m. current commutator
CO
(5) <[f™ix), yr(0)]>o = ijda*<>(cr*) (&„— ^ 3, W a*) .
o
We also pointed out how different assumptions on the finiteness or lack of
finiteness of relevant integrals involving ti(K 2 ) (or equivalently, involving the
spectral function q) would lead to statements on the asymptotic behaviour
of a(E). In particular, some observable effects are known to depend on
integrals
(6) J%^ d «
If one wants them to be finite, the integral (6) must be convergent or, equiv
alently,
(60 J«£?d*»<oo,
or, in terms of a{E)
(6") (dEE^(j(E) < oo .
Equation (6") implies a decreasing crosssection, a very weak statement
presumably. (Under such conditions the hadronic vacuum polarization cor
rections to g — 2 of the electron or of the muon, for instance, are finite.)
Highenergy e+e annihilation into hadrons 141
Table III.  Compound field algebra (CFA).
Z
oo — ^0
oo Z^O
J da 2 Q (a 2 ) = oo J ^ J w 2
We consider what we call the « standard realization » of CFA: m„ > oo and g > constant.
In this case I dcx 2 — — ~ ml and J da 2 g(a 2 ) ~ wj
g((T 2 )~'CT 2 asymptotically: o(s)~l/s 2 .
e.m. mass differences finite: infinite Schwinger term in [/„,/,]; infinite cnumber term in
A more stringent statement was derived in ref. [4] from the assumption that
00
(7) M Ua,
be finite. Such an assumption is connected to the possible finiteness of the
hadronic contributions to charge renormalization. From eqs. (3) and (4),
one would obtain
(70 j^Woo,
or equivalently
CO
(7") (dEEa(E)<oo.
The crosssection in this case would have to decrease faster than E~ 2 , say,
~£~ 2 (log£) 2 , etc.
3.  The spectral representation of eq. (5), taken at equal times, gives
directly
00
(8) S(xo)<[ti m <x)J e riO)]\ = (M,< + ^,«W(*)J^e(* a ) •
Equation (8) is one of a class of sum rules [13] that have been intensively
exploited during last years. Equation (8) can be taken as a proof for the
142 R. Gatto
existence of Schwinger terms in the commutator between a space component
and the time component of a local current. The conservation of the current
is irrelevant to such a proof. For a conserved current, Schwinger's original
argument [14], makes the argument quite transparent: The limit
(9) Jim < U(0), [H, j (x)]] > <5(x ) ,
vanishes only if j o (x)\0y = 0, i.e., for a vanishing current; for a conserved
current the limit is
(io) iimaKU(0),y*(*)]><A*o)
and its nonvanishing contradicts the naive calculation of the commutator
with currents taken as bilinear forms of fields at the same spacetime point.
One solution is to redefine the currents by introducing an infinitesimal space
like separation e^ between the arguments of the fields, to formally compute
the commutators, and to let s^ > isotropically (elimit procedure). This
procedure (which may still be deceptive because it is based on the unrenor
malized fields; see, however, our discussion later) suggests a quadratically
divergent vacuum expectation value for the Schwinger term
(ii) «w<[/oW,y«(o)]> ~^^).
We also recall that in quantum field theory Schwinger terms are seen to be
related to the socalled seagulls [15]. Such a relation follows here directly
from gauge invariance.
4.  Sum rules for higher moments of the spectral function
(12) (doW N Q (a 2 ),
can formally be obtained in terms of multiple commutators
(13) <[[...[[e,(0), P a ] P p ] ... P a ]W)]>o ,
where P^ is the total fourmomentum operator and Q / ,(t)^ij / ,(x)d 3 x.
Generally such sum rules will be divergent. Even so they may be of value
in suggesting the asymptotic behaviour of £>(cr 2 ) or, equivalently, of the cross
sections. To illustrate the derivation consider, for instance,
(14) C^Axo) = <[[[[G„(0), PJPp]Py\JM]> d(xo) =
=  iW^UAW^W^ ) + ;;(0)H 3 <5W;;(0)> , (p 4 = #0 •
Highenergy e + e annihilation into hadrons 143
Inserting the spectral representation, in the form in eq. (5), one can write
( 15 ) C^ yv d{x ) = — idixJd^dpid^d^dyjdoWQia 2 ) ,
which is the desired sum rule.
5.  The spectral function q(g 2 ) can be obtained from eq. (5)
(16) d(q) Q (qZ)q* = 1 ± Jd** exp [ ftpc] (^^ ~^) •
In the cm. frame
(17) Q{q)Q(q 2 )q 2 d(q) = d(q)± ± J d*x exp [ i?*]<#™<*)#">(0)>
which, among other things, exhibits clearly the relation written in eq. (4)
for each set of intermediate states F.
In applying the sum rules one may note that, in the lowest order electro
magnetic approximation that we are adopting here, one can separately treat
the isovector and the isoscalar terms in j% m : The sum rule in eq. (8) then
gives, calling 2E = s,
00
(18) <5(x )<Un*MnO)]> = 3 * <5 W< 5i,ov >o= i^s ^(x) fds ? s 2 a(*) isov
and a completely similar equation with « isovector » substituted by « iso
scalar ». In eq. (18) the Schwinger term has been called S. On the basis of
(asymptotic) SU 3 one can try to use the relation : 3 <5 iso8 > = <S isov > or
(19) \ds 2 s 2 [o is °v(s) — 3o isos (s)] = .
Equation (19) suggests a persistent oscillatory character of Ao= a isov ~3a' lsos ,
or a sharp decrease of such a difference. From the view point of saturation
with resonances it would not be unrealistic to think of a persistent simul
taneous occurrence of T= 1 and T=0 vector mesons with relations among
residue such that eq. (19) is satisfied.
The model for the currents we had examined in Sect. 4, in terms of bilinear
expressions in spin \ fields evidently suggests a quadratic behaviour in energy
of the divergent integral in eq. (18). This means a(s)ccs~ 2 for large s
144 R. Gatto
(remember, however, we are only including onephoton exchange). The
same result would obtain when including currents formed out of spin zero
bosons. Al alternative argument for such a behaviour follows from the
requisite of gaugeinvariance on the vacuum polarization tensor n^) The
gauge invariant form is notoriously [16]
(20) 7t MV (q) = ijtfxexp [iqxKTj„(x)MO)> tt Mi tyt/j^ Q(° 2 )
and gauge invariance requires
(21) <7„Jd 4 xexp [iqxKTj tl (x)j v (0)y o =d vi q i j ^ q(<7*)
The lefthand side of eq. (21) can easily be calculated in the renormalized
quantum electrodynamics of spin \ fermions and seen to be quadratically
divergent. A behaviour q{<j 2 )ozo 2 is equivalent to a(s)ccs~ 2 (recall that
s = 2E). The lack of covariance (besides gauge invariance) of the lefthand
side of eq. (21) is an example of a frequent situation with divergent
Feynman integrals. In the notation in eq. (18) higher moment sum rules
are of the form
CO
(22) < [[H, fir ]? ^ov ( 0)] >0 = _1_ j ds 2 s 4 ^isov,
CO
(23) < [H[H, &rl 7? ov (0)] > = r ^ 2 jds*s« o( S ) is °\
and quite similar equations with « isoscalar » substituted for « isovector ».
When applied to a model of bilinear currents from spin ^ fermions these
equations appear all consistent with the above behaviour, q(g 2 ) oc <t 2 . (Of
course the result may not hold when singular interactions are present.)
6.  A rigorous Lagrangian scheme of vector dominance, including proper
treatment of gaugeinvariance, is that of Kroll, Lee and Zumino [17]. It rests
on the idea of fieldcurrent identity. To illustrate the main point let us limit
ourselves to the pmeson and its strong interaction. The Lagrangian density
is supposed to be of the form
(24) \rn 2 2,Q»+2",
=
o,
™ 2 ^
5
Highenergy e + e~ annihilation into hadrons 145
where <£' is invariant under g fi ^Q ft + g^d^A and a corresponding trans
formation on the matter fields. The (gaugeinvariant) prescription is ^^
>Q fl \(e/g)A fl inside j§?' (of course only isovector photons are included).
The equations of motions
(25)
(26)
establish the required fieldcurrent identity. One performs a wavefunction
renormalization q° = ^/Zq^ and introduces Z = (m/m ) 2 . The renormalized
and unrenormalized sources J v and J® for the pmeson are directly related
(27) /o = /v+(1 _ Zo) I^ = _ 2 L ±^\
where G^,, is the field tensor for the pmeson and g its renormalized coupling.
(One conventionally defines the unrenormalized coupling as g = gi/ZZo 1 .)
The important observation is that for m —»oo, the e.m. current (identical
as we have said to the field) becomes identical to the unrenormalized current /° .
This situation, currentcurrent identity, had been studied by GellMann and
Zachariasen [18]. Always limiting to the above Abelian case one verifies
how the spectral function sum rules now follow from the canonical com
mutators and the field equations. For instance, the sum rule in eq. (22'
follows directly from the spectral representation
(28) <[<?„*(*), <?,(0)]> = ijd0*Q(o*y(d x ,d f  d^dJAix, **)
and the canonical commutator
(29) %xJ[G H (x), <?,(<>)] = 1 dijdix) .
The non Abelian situation (SU 2 , SU 2 xSU 2 , SU 3 , SU 3 xSU 3 ) [11] presents a
formal difficulty connected to the occurrence of ambiguous terms propor
tional to bilinear expressions in the gauge fields taken at the same spacetime
point in commutators of fields and their time derivatives. Such products are
not well defined, nevertheless they presumably contribute a vanishing vacuum
expectation value. [A rough argument is: {^^(x) <p v ( x )}o should be pro
portional to d^ on the basis of covariance, but ^(p i (x)(p i (x)') and <<Mx)<M*)>
10
146 R. Gatto
have opposite sign. Furthermore in the nonAabelian cases (escluding SU 2 )
some currents are not conserved.
7.  In spite of the above remarks for the nonAbelian case we think it is
useful to take the following attitude. We consider a general YangMills
theory and include in the discussion its limiting cases. This provides for a
classification in terms of convergence or lack of convergence of the sum
rules or, if one prefers, in terms of asymptotic behaviours of the e + e~ anni
hilation crosssection. Alternatively one can present the classification in terms
of limits on the bare quantities m and g . (We have already discussed one
realization of the situation ra ^oo.) We shall briefly distinguish three cases:
1) finite field algebra (FFA);
2) divergent field algebra (DFA);
3) compound field algebra (CFA).
The three cases, 1), 2) and 3), are illustrated in Table I, II and III.
From the point of view of the crosssections we thus have:
1) FFA: a(s) decreases faster than s~ 6 ;
2) DFA: a(s) decreases faster than S 4 ;
3) CFA: in the standard realization a(s) decreases as s~ 2 .
Note that only in FFA and in DFA one has a finite A'^. In DFA and
CFA mQ^oo, i.e., the bare mass is infinite. The finiteness or lack of finite
ness of the spectral integrals is a direct reflection of the respective finiteness
or lack of finiteness of the two cnumber terms appearing in the commutators
K*o) L/«o(*), 7/ji(0)] and S(x ) [d j ai (x) — d t j a0 (x), j pi (0)] .
In the latter commutator, besides a ^number Schwinger term tranforming
as the component of a fourvector and thus irrelevant here, there also appears
a ^number (5function contribution which transforms as a reducible tensor.
This last term is responsible for the e.m. mass differences [19]. Finally we
note that the standard realization of CFA gives for the spectral integrals a
behaviour identical to that obtained from currents bilinear in spin \ fer
mion fields. (If one wants one can call them « quarks » considering the cur
rent inflation in the use of such a word.) That the limit of vanishing renormal
ization constants is relevant to a composite particle picture emerges also
from a number of field theoretic investigations [20, 21]. We note that CFA
came of interest to us to discuss the higher weak orders in our theory of the
Cabibbo angle [9]. An extension of these concepts along the lines of Wilson's
approach to field theory [22] and employing approximate scale invariance
has recently been developed [23].
Highenergy e + e~ annihilation into hadrons 147
REFERENCES
[1] F. Arnman, R. Andreani, M. Bassetti, M. Bernardini, A. Cattoni, V. Chimenti,
G. F. Corazza, D. Fabiani, E. Ferlenghi, A. Massarotti, C. Pellegrini, M. Pla
cidi, M. Puglisi, F. Soso, S. Taffari, F. Tazzioli and G. Vignola: Lett. Nuovo
Cimento, 1, 729 (1969). See also the pioneering work with Ada, by C. Bernardini,
G. F. Corazza, G. Ghigo and B. Touschek: Nuovo Cimento, 18, 1293 (1960).
[2] See for instance J. E. Auguston et ah: Phys. Rev. Lett., 20, 129 (1968); V. Auslan
der et al: Phys. Lett., 25 B, 433 (1967).
[3] N. Cabibbo and R. Gatto: Phys. Rev. Lett., 4, 313 (1960).
[4] N. Cabibbo and R. Gatto: Phys. Rev., 124, 1577 (1961).
[5] J. D. Bjorken: Phys. Rev., 148, 1497 (1966).
[6] J. Dooher: Phys. Rev. Lett., 19, 600 (1967).
[7] J. J. Sakurai: in Proceedings of the 4th International Symposium on Electron and
Photon Interactions at High Energies, 1969, Daresbury Nuclear Physics Laboratory,
Daresbury, Lancashire.
[8] M. Gourdin: Boulder Lectures (1969).
[9] R. Gatto, G. Sartori and M. Tonin: Phys. Lett., 28 B, 128 (1968); Lett. Nuovo Ci
mento, 1, 399 (1969). See also: R. Gatto: Cabibbo angle and SU 2 xSU 2 breaking,
Springer Tracts in Modern Physics, vol. 53, SpringerVerlag, Heidelberg (1970).
[10] C. N. Yang and R. L. Mills: Phys. Rev., 96, 191 (1954).
[11] T. D. Lee, S. Weinberg and B. Zumino: Phys. Rev. Lett., 18, 1029 (1967).
[12] G. Kallen: Helv. Phys. Acta, 25, 417 (1952); H. Lehman: Nuovo Cimento, 11, 342
(1954).
[13] S. Weinberg: Phys. Rev. Lett., 18, 507 (1967).
[14] J. Schwinger: Phys. Rev. Lett., 3, 296 (1959).
[15] R. P. Feynman: unpublished.
[16] V. N. Gribov, B. L. Ioffe and I. Ya. Pomeranchuck : Phys. Lett., 24 B, 554 (1967).
[17] N. Kroll, T. D. Lee and B. Zumino: Phys. Rev., 157, 1376 (1967); T. D. Lee and
B. Zumino: Phys. Rev., 163, 1667 (1967).
[18] M. GellMann and F. Zachariasen: Phys. Rev., Y2A, 953 (1961).
[19] S. Ciccariello, G. Sartori and M. Tonin: Nuovo Cimento, 55 A, 847 (1968).
[20] K. Hayashi, M. Hirayama, T. Muta, N. Seto and T. Shirafuji: Fortschritte der
Physik, 15, 625 (1967); S. Ciccariello and M. Tonin: Nuovo Cimento, 58 A, 43
(1968). It was conjectured by A. Salam: Nuovo Cimento, 18, 466 (1960) that the
condition of vanishing renormalization constants is a fieldtheoretic formulation of
the bootstrap principle.
[21] The possible limits for m ^0 of the YangMills theory are also of great interest:
see R. Brandt and J. D. Bjorken: Phys. Rev., Ill, 2331 (1968) where the connection
with the Sugawara model is also discussed.
[22] K. G. Wilson: Phys. Rev., 179, 1499 (1969).
[23] S. Ciccariello, R. Gatto, G. Sartori and M. Tonin: Phys. Lett., 30 B, 546 (1969);
and Padua preprint (to be published). R. Gatto, Rivista Nuovo Cimento 1, 514, (1969).
New Frontiers of HighEnergy Physics.
G. GlACOMELLI
CERN  Geneva
INFN, Sezione di Bologna  University of Bologna
1.  Introduction.
One of the « frontiers » of physics has been and will be the study of phe
nomena at always decreasing small distances. Progress in this field has been
swift: The frontier passed from the study of molecules to that of atoms,
then to nuclei and to elementary particles. In terms of distances, one passed
from distances of the order of 10~ 8 to 10 14 cm. The present frontier is the
study of the socalled elementary particles; in particular we want to know
if they are really elementary or composite.
The progress has always been connected with the development of new
accelerators of ever increasing energies. They allowed the production of
secondary beams of higher energies and of beams of altogether new particles.
Atomic phenomena could be studied with photon and electron beams of
eV energies. The study of nuclear phenomena required beams in the MeV
range and new types of accelerators: Cockroft Walton's, Van der Graafs,
cyclotrons, and betatrons produced the appropriate proton, electron, and
photon beams. Another energy step and different types of machines were
required before the new field of elementary particles could be entered ; new
types of objects, unstable ones, were produced, which did not exist in nature.
Synchrocyclotrons and electronsynchrotrons produced tz mesons ; the 3 GeV
Brookhaven cosmotron produced Kmeson beams and allowed the study of
various hyperons. At the 6 GeV Berkeley bevatron the antinucleons were
discovered. The 28 GeV CERN Proton synchrotron (PS) and the 33 GeV
Brookhaven AGS, together with some of the lower energy machines, brought
into full swing the study of the resonances between various types of particles,
and allowed the production of new objects, such as the muon neutrino. The
highenergy frontier is at the moment represented by the 76 GeV Serpukhov
New frontiers of highenergy physics 149
IHEP accelerator, while colliding beam machines are opening up a com
pletely new field.
The increase in energy between 1 eV to 33 GeV has brought about the
discovery of three types of spectroscopies — the atomic, nuclear, and particle
spectroscopies — whose study is best done with beams of appropriate energies :
(1H000) eV for atoms, (0.1^10) MeV for nuclei, (0.1 MO) GeV for par
ticles. The energy regions in between may be considered as transition energies
or asymptotic regions for the preceding spectroscopy. The 76 GeV machine
seems to cover such a type of asymptotic region for particle physics.
The race toward higher energies will have as the next steps the 400 GeV
proton accelerator of Batavia, and the European 300 GeV. A glimpse of
what is going to happen at much higher energies will be offered by the CERN
25 GeV pp ISR colliding beam machine and the 20 GeV pp Novosibirsk
machine.
Professor Edoardo Amaldi works on the frontier, in particular looking
for new phenomena [1], and he has been since a long time the Chairman of
the European Committee for Future Accelerators (ECFA). It is also because
of his efforts that European laboratories can work right on the frontier of
highenergy physics.
In this note we shall discuss the recent beginning of the exploitation of
the 76 GeV IHEP accelerator, comparing layouts and the first experimental
results with those from CERN and BNL. Finally, we shall make some con
siderations and extrapolations for the future accelerators.
2.  Accelerator beams.
The experiments that can be performed at an accelerator depend criti
cally on the quality and quantity of the available secondary beams. In a PS,
the beams may originate either from an internal target or from a target
placed in an extracted proton beam. While the first system was used exten
sively in the past, the trend for the future seems to be that of switching from
internal to external targets. The main reasons for this trend are connected
with problems of radiation damage, which become serious when accelerators
reach 10 13 protons per pulse (ppp); moreover, external beams offer greater
flexibility. On the other hand, beams originating in an internal target may
have better optical qualities, because of the smaller transverse dimensions
of the source.
Table I offers a comparison of the CERN and IHEP accelerators.
The absence of long straight sections in the IHEP accelerator means that
most of the secondary particle beams pass through the magnetic field of the
150 G. Giacomelli
Table I.  Some characteristics of the 28 GeV CERN Proton Synchrotron and of the 76 GeV
IHEP Proton Synchrotron. 1972 projected values represent rough estimates. Of the two
numbers indicating the number of beams, the first gives the actual number of beams,
irrespective of branches, while the effective number of beams is computed using the Brook
haven criteria, keeping in mind compatibility of operation and number of branches:
i) a beam with two or more branches is worth 1.5 beams; ii) compatible beams are worth
one each, while two noncompatible ones are worth only 1.
Machine CERNPS IHEP
Year 1969 1972 1969 1972
(projected) (projected)
Maximum energy 28 GeV 28 GeV 76 GeV 76 GeV
Normal energy for counter experiments 19 GeV 25 GeV 70 GeV 70 GeV
Average intensity per pulse 10 12 10 13 10 12 5 x 10 12
Repetition rate 2.4 sec 2 sec 7 sec 7 sec
Maximum burst length 0.5 sec 0.5 sec 1.0 sec 1.5 sec
Total number of counter beams 12 15 3 7
Effective number of counter beams 6 7 34
Total number of bubble chambers 3 4 3
Number of fast extracted proton beams 1 2 — 12
Number of slow extracted proton beams 12 1
machine. Therefore it is difficult to have more than one beam coming from any
one internal target, and it is more complicated to get positive beams. Two
negative beams and a neutral one, each originating from a different target,
are in use in a single large experimental area. One of the charged beams
(No. 2) covers the range (40^65) GeV/c, while the second one covers the
range (25^40) GeV/c. Each of them has several possible branches. Beam
sharing among the three beams as well as with an internal facility is possible.
CERN has two main experimental areas, one fed by internal targets and the
other by external beams. The two counter areas cannot operate at the same
time, while instead one or two bubble chamber can parasite for most of the
time. Both laboratories have improvement programmes, as illustrated in
Table I.
A neutral beam may be made with only a collimator and a sweeping
magnet. Instead, a charged particle beam requires a large number of quadru
poles and bending magnets; it is then possible to achieve beams of really
good optical properties. For instance, the IHEP beam No. 2, which is the
highest energy beam available at present, may yield 10 6 7r of 40 GeV/c per
burst with a momentum acceptance of ±10% and horizontal and vertical
acceptances of 3 mrad each.
Q
<
<
10"
io
XT
<
XT mr
10
,6
A
1
a)
P =70GeV/c
P =550GeV/c
0=4 mr
A
6000
t,
6500
N
7000
10
10"
in
in
in
^4rt3
^knXTh
to
Hto
in
cgl/)
■vA
mio 
nn r r
X)" 5 h
0*
Tl"
P =70 GeV/c
P=A5GeV/c
0=5 mr
1500 1700 1900 2100
N
u
in
m
va
in
in
eg
in
xr
xr
in
in^.
in
«n
K)"
XT
tf
/rT
W
c)
$=70GeV/c
P=50GeV/c
0=1Orar
/ ~J£^.
r~
r
\i
02 QA 0.6 08 1.0
fi,(C,C 2 ) [at]
fg=70GeV/c
P=40GeV/c
0=Omr
02 04 0.6* 0.8 10 1.'2'
P N (C;C ? ) [at]
Fig. 1 .  Pressure curves (or mass spectra) at different beam momenta obtained
with: a), b) differential Cerenkov counters, c) a combination of three threshold
Cerenkov counters, d) a counter in the differentialthreshold mode of operation.
152
G. Giacomelli
3.  Particle separation at high energies.
Typical particle ratios in a negative, highenergy (*) unseparated beam
are: tc(1), [x(10 2 ), K(10 2 ), e(10 3 ), p(10 3 ); and in a positive beam:
p(10), 7u+(100), ^.+(102), K+(10 2 ), d(10 2 ), e+(10 3 ). Since one is usually
IT
A
10T6
K"
n
12000
16000
20000
N
Fig. 1.  Pressure curves (or mass spectra) at different beam momenta obtained
with: e) a combination of three Cerenkov counters in the threshold mode trig
gering a differential counter [2].
(*) In the following high energy will usually mean more than 510 GeV.
New frontiers of highenergy physics 1 53
interested in only one of them, the problem arises of removing the others.
Unwanted particles may either be physically removed by means of separators
or simply not counted by electronics means.
The only types of separators available for highenergy beams are radio
frequency (RF) separators, which at the moment can be used only for bubble
chamber beams, that is for beams of short timeduration.
The electronics separation of different types of particles is usually per
formed by timeofflight techniques or by means of Cerenkov counters. The
timeofflight technique is limited by the present capability of resolving about
0.2 nsec. Many types of Cerenkov counters have been used for particle sepa
ration at highenergy [2]. The best resolutions achieved so far are of the
order of A/? < 10~ 5 . Great care has to be exercised to achieve these resolutions:
Threshold Cerenkov counters have to be many metres long; in differential
counters, the Cerenkov light has to be chromatically corrected and the beam
has to be quite parallel, so that a good performance of the Cerenkov counter
also indicates an optically good beam. In a counter built at CERN, the
index of refraction of the gas was measured by means of a laserrefracto
meter, providing an absolute measurement of the particle velocity and hence
of the mass of the particle [2].
Figure 1 shows pressure curves at different momenta obtained by means
of differential a), b), threshold c), differentialthreshold d), and a combination
of threshold and differential Cerenkov counter e). These curves show that
present Cerenkov counter techniques allow the separation of kaons, when
in 0.1% abundance, from pions up to 60 GeV/c (Fig. laId), and that a
combination of Cerenkov counters is capable of rejection ratios of better
than 109 (Fig. \ e ).
4.  Particle production.
One of the first experiments to be performed at a new accelerator is a
measurement of the yield of different particles. These measurements are
important both for practical purposes, as for instance the need for information
for beam design, and on the techniques necessary to identify the particles,
as well as to understand the physics of particle production at high energies.
Photon production is easily measured by means of a glass total absorption
Cerenkov counter [3] or a sandwichcounter, where scintillator plates are
alternated with lead plates. These systems are really total absorption calori
meters, where the total energy lost is simply given by a pulseheight meas
urement.
A study of the production of charged particles requires a system of
Cerenkov counters as described in the previous chapter. Figure 2 shows a
154
G. Giacomelli
10"
10~ 3
5_
K7tT
^n8
v\
\
\
• o
o
P/TT
\
♦\
• o
E =70 GeV
A
52GeV
7
43 GeV
a
3 5 GeV
+
20GeV
19.2 GeV
\
0.4
0,6
0.8
P/P A
1.0
Fig. 2.  Particle ratios R vs. secondary beam laboratory momentum divided
by the kinematically allowed maximum momentum of the heavier particle
(K~ and p, respectively). The points represent the results of measurements per
formed at the IHEP accelerator operated at various energies [2]. Points corre
sponding to the same incident energy and secondary momentum correspond
to different angles of production. The broken line represents the 19.2 GeV
CERN data [4] for pp collisions, which coincide with the dependence found
by the same group for pAl collisions. E = 70 GeV (• o), 52 GeV (a),
13 GeV (v), 35 GeV (.), 20 GeV (+), 19.2 GeV ( ).
New frontiers of highenergy physics
155
o
» 10 " ;
E
oft
10 a
PARTICLE PRODUCTION
p*p,19.20GeV/c
12.5 mrad (LAB.)
12
P (GeV/c)
Fig. 3.  Laboratory spectra for n ± , K ± , p, and p produced in 19.2 GeV/c
protonproton collisions at 12.5 mrad laboratory angle [4]. The horizontal scale
gives the secondary laboratory momentum, while the vertical scale gives the
double differential crosssection in the laboratory frame.
156 G. Giacomelli
compilation of negative particle ratios produced when the internal beam of
energy between 20 and 70 GeV strikes an aluminium target [2] ; the variable
on the abscissa is r\ = p/p ma x, the secondary beam momentum divided by
the maximum momentum the heavier particle (K _ , or p) may carry, assuming
the usual conservation laws of charge, baryon number, and strangeness.
When plotted vs. rj, the particle ratios change very little from 20 to 70 GeV
for large values of 77, while they increase slightly for smaller values of r\. It is
interesting to notice that the ratio of K to tc production remains small, even
at energies so much larger than kaon threshold [2].
« Pionization », that is the production of a large number of pions, seems
to be the dominant result of highenergy protonproton collisions.
The measurements of the absolute fluxes from an internal target cannot
be very precise; moreover the theoretical analysis is complicated by the
presence of a complex nucleus. Refined measurements require an external
proton beam and a liquid hydrogen target [4, 5]. Figure 3 shows the results
of a recent CERN experiment performed along these lines.
Several production models have been proposed: They range from the
statistical model with collective motion corrections [6], fireball mechanisms [5],
etc., to semiempirical formulae of the types of Cocconi and Perkins [7].
These models give, for particle spectra, equations with a number of
parameters to be determined experimentally. All the models are able to
predict the pion data reasonably well, while the predictions of the kaon and
antinucleon spectra are poorer. These models may at present be used as
guiding lines, but are not expected to be very reliable at higher energies.
5.  Crosssection measurements.
The simplest crosssection measurement is the total crosssection; then
follow, in order of complication, the elastic crosssection in the diffraction
region, several twobody processes, etc.
5T. Total crosssections.  On the basis of the behaviour with energy of
the total crosssections, one may speak of two energy regions, the resonance
and the highenergy regions, respectively [8]. In the first region (below 5 GeV),
the total crosssections are characterized by the presence of structures, most
of which may be interpreted as resonances. In the highenergy region the
total crosssections are slowly varying functions of the energy and do not
exhibit any appreciable structure. We shall be concerned with crosssection
measurements in the second region. What is of interest here is the energy
behaviour of the crosssections and the relations among them. It was ex
pected that in the limit of very high energies, hadron collisions do not depend
New frontiers of highenergy physics
157
on the nature of the interacting particles, nor on the specific mechanism of
strong interactions. In particular:
a) the ratios between the various total crosssections should be governed
by some internal symmetry;
b) the total crosssections of the particles belonging to the same isospin
multiplet; and
c) the total crosssection of particle and antiparticle should become
equal (Pomeranchuk theorems [9]).
More specific models predict the behaviour of the crosssections as functions
of energy. At present their predictions are contradictory: some models predict
that the crosssections decrease toward constant nonzero values [10]; others
predict that the crosssections go to zero as the energy goes to infinity [11];
finally other models predict that the crosssections reach a minimum and then
rise to finite asymptotic values [12].
Figure 4 shows a compilation of the highenergy total crosssections [8],
including the recent CERNIHEP results at the 76 GeV synchrotron [13].
t AS
HMORE
60
i
GftLBRAIT
H 65
M 65 PN
V 11
NDEMBAU
M 61
}
C1TR0N
65 TIN
t Dl
DDCNS
62
i
BUGG
66 PN
\ "
VENKO
62
t
FOLEY
67
{ "'
OOENS
63
t
ALLABY
69
2 3 4 50
LABORATORY MOMENTUM (GeV/)
Fig. 39
Fig. 4.  A compilation of highenergy total crosssections [8]. Data points are
shown only for pp, pp, n~p, K~p, and K + p. The lines represent the results of
the least squares fits of the total crosssections above 5 GeV/c to the equation
158 G. Giacomelli
The total crosssections for 7c~p, 7in (= rc+p), K~p and K~n seem to
have become energy independent in the region above 30GeV/c; the K + p
and K + n crosssections are already constant between 10 and 20 GeV/c, while
the pp and pn crosssections are still decreasing at 50 GeV/c.
The total crosssections on protons and neutrons have become almost
identical, suggesting that at these energies the strong interaction crosssections
are almost independent of isospin. The K~p and K + p total crosssections
do not seem to come together as the energy increases.
The available highenergy data may be fitted to simple empirical formulae
of the type:
(!) ffOlab) = cr(oo) + j ,
/>lab
( 2 ) o"Oiab) = apf ab .
The fittings to eq. (2) give worse % 2 than the fittings to eq. (1), suggesting
that the data are in better agreement with finite asymptotic crosssections.
Table II gives the results of fitting the available data above 5 GeV/c to eq. (1)
for d = 1 . Both statistical and systematic errors have been taken into ac
count by combining them quadratically. It is not clear how the differences
between K~pK + p and may be between pppp can be reconciled within the
framework of the existing theories. Also: the available data do not allow
a definite conclusion about which model predicts correctly the energy be
haviour. More experimental data are clearly needed.
Table II.  Least squares fits of total crosssections to the formula a = c + cJpi^ for
P\ab> 5 GeV/c [8]. In order to obtain more satisfactory x 2 the systematic errors have
been compounded quadratically with the statistical ones. No x 2 's are given for the K~n
and pn, since the fits come from interpolated data.
Total cross
Number
section
c°
Cl
X 2
of points
TTp
23.89 ± 0.04
27.56 ± 0.50
57.6
84
tc+p and
n~n
22.78 ± 0.06
19.40 ± 0.60
35.8
66
Kp
20.18 ± 0.18
24.63 ± 2.22
22.1
30
K~n
19.49 ± 0.31
6.13 ± 3.08
—
18
K+p
17.44 ± 0.24
 0.22 ± 2.42
31.6
20
K+n
17.63 ±0.41
0.55 ± 3.54
—
11
PP
42.44 ± 0.42
108.3 ± 6.1
24.8
24
pn
42.48 ± 0.74
87.6 ± 8.2
—
17
PP
38.29 ± 0.08
15.24 ± 0.87
27.1
52
pn and
np
36.48 ± 0.74
27.3 ± 5.9
21.9
16
New frontiers of highenergy physics 159
The quark model prediction that the asymptotic 7rJV total crosssection
is f of the asymptotic pJ\P crosssection, can be compared with 0.62, as obtained
from Table II.
5*2. Elastic crosssections.  The elastic crosssections are either slowly
decreasing or remain constant as functions of energy. This means that the
opacities, defined as the ratios of elastic to total crosssections, are either
constant or slowly decrease with energy.
The elastic angular distributions may be subdivided into three regions:
a) the very small angle region where Coulomb and nuclear scattering
interfere ;
b) the diffraction region proper; and
c) the largeangle region, characterized by very small crosssections.
Large counter hodoscopes or large spark chamber arrays are usually
employed for measuring the elastic differential crosssection. A simpler
experiment was recently performed at the IHEP accelerator by bombarding,
with the internal proton beam, a polyethylene target [14] (*). The recoiling
proton was detected by means of solidstate detectors, which measured angle
and range. It was thus possible to separate elastic from inelastic events in
the \t\ range (0.01^0.11) (GeV/c) 2 for proton incident momenta from 12
to 70 GeV/c. In this angular region the diffraction pattern is well [represented
by an exponential (Fig. 5):
(3) £«M
where the slope b changes monotonously from 6^10 (GeV/c) 2 at 12 GeV/c
to b = 11.5 at 70 GeV/c (Fig. 6). Thus the shrinking of the diffraction peak
initiated at energies around 5 GeV, continues when the energy is increased.
Only higher energies will be able to tell if the shrinking goes on or eventually
saturates. Within the framework of the Reggepole theory, the elastic scatter
ing data may yield the slope of the vacuum (Pomeranchuk) trajectory, which
is found to be oc P = 0.40 ± 0.09 [14].
In another perspective the small angle elastic scattering is considered to
arise from a diffraction mechanism, as the shadow of all the inelastic processes.
In this framework, the simplest classical nonrelativistic optical model
(*) In the future the polyethylene target will be susbstituted with a gaseous jet of
hydrogen at supersonic speed, and the experiment will cover the Coulombnuclear inter
ference region.
160
G. Giacomelli
*
1.0
0.8
lQ.6
(0.4
0.2
fill
58.1 T38
1L=H07t0.18
$
%
0.01
0.05
0.10
*( J
Fig. 5.  The differential protonproton elastic crosssection at a laboratory
kinetic energy of 58.1 GeV in the 0.0K f< 0.11 (GeV/c) 2 range [14].
(opaque dis) [8], predicts that the interaction radius, given by
(4)
2Vb,
grows from 1.23 to 1.34 fm.
In more sophisticated optical models the size of the proton remains con
stant; the shrinking of the pp diffraction pattern may then arise from the
Lorentz contraction of the colliding particles in their direction of motion.
The antishrinking of the pp elastic peak requires other hypotheses, such as
that the total crosssections are still decreasing and therefore one is nowhere
near an asymptotic behaviour.
The opinion on the large angle scattering is even more divided: some
authors suggest that it is purely diffractive, possibly arising from different
spatial structures inside the nucleon; other authors suggest that a statistical
mechanism may play some role.
New frontiers of highenergy physics
161
8,<oev/c)"*
12
10
• thisexpeziment
o  n.* KMPHnnOBA M AP. HM6HA H965r)
o G.BrteeHtnletae.CERN(1965r)
a  k.i. FoCey. w aC. Bzookhaven tt963r)
uUS
V
h
m
I)
.\P
8 10
20 30
50 70
Ertn&SP**'
Fig. 6.  The coefficient 6 of eq. (3) for protonproton elastic scattering in the
diffraction region [0.0K /< 0.1 (GeV/c) 2 ] vs. laboratory kinetic energy [14].
5*3. Other crosssections.  The study of charge exchange crosssections
is particularly important because their theoretical analysis is simple, at least
in the context of Reggepole theory, where only one exchanged trajectory
explains the main features of the data. Present experimental information
stops at 18 GeV, but experiments will soon be done at higher energies.
Most of the available experimental results on the more sophisticated
measurements are still not systematic, though a wealth of information is
available.
It is clear that one is nowhere close to an understanding of strong inter
actions and that more and more experiments, particularly at higher energies,
are required.
It may come as a surprise to learn that at the very high energies con
sidered in this report, one may still obtain information on nuclear properties.
The absorption crosssections a a measured at 20 to 50 GeV/c with incident
K~, 7T _ , p, and d on a variety of nuclei have revealed that their dependence
on the atomic number A is of the form [8, 13, 15] (Fig. 7):
(5)
a = a n A c
162
G. Giacomelli
where a = 0.76, 0.75, 0.67, and 0.67, respectively for K", tc" p, and d. The
large value of a for particles with small elementary crosssections (K~, n~)
may be explained qualitatively as being due to the fact that light nuclei are
G q .10" 27 cm*
2000
1000
500
200
100
50
Li Be C
Al
Cu
Sn
PbU
Fig. 7.  Nuclear absorption crosssection for K~, it~, p at 40 GeV/c [13] and
d at 25 GeV/c [15]. The lines represent the results of the least squares fits ac
cording to eq. (5); p = 40 GeV/c.
not completely black for KT and n~. The antiprotons instead behave as if
hitting a completely black nucleus (for which x should equal f). The d cross
sections, though poorly known, are very large, indicating both the large size
of the antideuteron as well as a sensitivity to the nuclear matter density at
the periphery of the nucleus.
New frontiers of highenergy physics 163
6.  Limits on new phenomena.
The discovery of new phenomena is one of the most exciting results of
the race towards higher and higher energies. When a new energy region be
comes available, a number of crude upper limits on new phenomena can
be easily obtained as byproducts of standard measurements. For instance,
from the pressure curves of Fig. 1 one has upper limits for the production
of negatively charged objects, in a rather ample mass region. Specific exper
iments are then required to refine these limits.
Physicists have invented a number of particles which could exist but have
not yet been found: the quarks, the intermediate vector boson, antiparticles,
tachions, magnetic monopoles, etc. Maybe these objects do not exist; maybe
they have large masses, so that present accelerators are not capable of pro
ducing them. We shall now discuss some of the recent limits at the highest
energies. Measurements concern only differential crosssections over specific
ranges of energies and angles; therefore estimates of the upper limits for
the total crosssections are necessarily model dependent.
6'1. The quarks.  The quarks were invented to explain the grouping of
particles and resonances in unitary singlets, octets, and decuplets. Many
searches were performed, employing accelerators, cosmic rays, and bulk
matter methods. The quark detection is based on the fact that the charge
of the quarks is fractional, for instance ±i or dzf ; therefore they ionize
less than minimum ionizing particles ( and f , respectively) and their ap
parent momentum is larger than the momentum of normal particles. In
particular, it is possible to have quarks with an apparent momentum larger
than the momentum of the accelerator. Using these last properties, the two
most recent experiments at the CERN and IHEP accelerators have yielded
the limits quoted in Fig. 8 [1618]. Although the limits have been computed
for charges ±, ±f the experiments are usually sensitive to charges in the
range 0.3^0.8 times the electron charge.
The interpretation of the limits quoted in Fig. 8 are ambiguous among
several possibilities:
a) quarks do not exist as physical entities;
b) the conservation of some quantum number prohibits their existence
as free entities;
c) they are so massive as to be beyond the energies available at the
present accelerators.
Ambiguities of this type will be with us in any unsuccessful search for
new objects.
164
G. Giacomelli
234501 234501 2301 23
QUARK MASS [GeV]
Fig. 8.  Summary of quark production data from accelerators [18]. The total
crosssections are expressed per nucleon and have been calculated assuming iso
tropic cm. angular distributions and fourbody phase space according to JY\JV >
^JNTJV + QQ. The « diagonal » curves represent the statistical model pre
dictions. The curves AF come from earlier experiments; curves H from [16]
and curves G and / from [17].
A recent cosmic ray experiment reported indications for the existence
of quarks of charge § [19]. A Wilson cloud chamber was triggered by a
system of scintillation counters sensitive to large airshowers, initiated by
extremely highenergy particles, estimated at about 10 6 GeV. A few low
ionizing particles were found in the core of the showers. This experiment
seems to have been now contradicted [20].
6*2. Heavy objects with unit charge.  Limits on these objects are obtained
from Cerenkov pressure curves such as those in Fig. 1 [2], or from timeof
flight measurements [2, 21]. The last method is particularly useful for heavy
mass objects, especially when triggered by Cerenkov counters which veto
light particles. A rough summary of the upper limits obtained in negative
beams with momenta between 25 and 40 GeV/c at 70 GeV primary energy
is the following: The production crosssection a m for masses m in the range
m n <m<m^ is a m <l0~ 7 a n while, for m^< m< (5^6) GeV, it is a m <
< lO 9 ^, where a n is the pion production crosssections.
The antideuteron yield increased by almost an order of magnitude when
the energy was raised from 30 to 70 GeV, and one may now work with about
one d per minute. It is likely that much will be learned about antinuclei
New frontiers of highenergy physics 165
in general at future accelerators, as indicated by the first absorption cross
section measurements for d [15] and the succesfull finding of few events
of 2 He [22].
6'3. Intermediate vector boson.  It is attractive to consider that weak
interactions are mediated by a vector boson, the w. The smallness of the
K$— Kg mass difference suggests that the w wass cannot be very large, while
neutrino experiments indicate that it must be greater than about 2 GeV [23].
At Brookhaven, a number of experiments have investigated, without
success, the mass region (2^5) GeV, by looking for muons produced at
large angles by the decaying boson [24] or by determining the intensity and
the polarization of muons originating very near to the point of interaction
of 28 GeV protons with uranium nuclei [25]. The last experiment quotes
an upper limit of Ba w < 6x 10~ 36 cm 2 , where B is the branching ratio of the
w into fi+v.
At very high energies, the relativistic time dilatation makes the n and
K mesons less liable to decay. Therefore, the muon contaminations in par
ticle beams will become smaller, and one can obtain a direct limit of the
number of \i mesons produced directly at the target. At the Serpukhov ac
celerator such simple limits are at the level of 10~ 3 ^10 4 of the pion flux
at the same energy and angle. These limits are adequate only for excluding
a strong production of the intermediate boson.
6'4. Magnetic monopoles.  The possible existence of a magnetic pole
would have some appealing aesthetical implications:
a) it would reestablish the symmetry between electric and magnetic
charges in Maxwell equations, in a formal way, not in a numerical
way, since the magnetic pole strength is probably so much greater;
b) it would provide some understanding of why the electric charge is
quantized; and
c) of why the photon mass is zero [1].
Also the experimental implications would be quite interesting:
a) the monopole would ionize thousands of times more than a min
imum ionizing particle;
b) it would be easily accelerated to thousands of GeV;
c) it could be « stored » in some materials, and so on.
A very complete review of monopole properties as well as of the present
situation about its existence can be found in the review article by Amaldi [1].
Here we shall discuss further possibilities.
The methods for detecting magnetic monopoles, at accelerators are usually
based on the fact that they curve toward the poles of a magnetic field, that
166 G. Giacomelli
their ionizing power is larger than that of fission fragments, and that the
ratio of Cerenkov to ionization loss is different from that of ordinary par
ticles [1]. A simple detector is a plastic material, placed a few centime
tres downstream from a target in a magnetic field: only heavy ionizing
objects which get bent towards the poles can be detected. The fission frag
ments, already present in natural plastic materials, provide a calibration of
the ionization, though they have to be removed (by heating) in order to
reduce the background. A crude test on these lines performed at IHEP gave
an upper limit of 10~ 38 cm 2 for monopole production.
6' 5. Tachions.  In nature one finds massive particles that travel at speeds
smaller than light and massless particles that travel at the speed of light.
The question arises: is it possible to have particles which travel faster than
light? Theoretically it is possible [26]: These objects would have an un
observable imaginary mass, they would gain velocity while losing energy
and, since they travel faster than light, they should produce Cerenkov ra
diation also in vacuum. Finally, they would end up as transcendent tachions,
with infinite velocity, zero energy, and a constant momentum [26]. Their
theoretical interpretation requires that they travel backward in time, like
antiparticles ; present theories may have problems with unitarity.
Tachions could be produced at accelerators, very likely with velocities
not too different from light. Actually the situation should be symmetric
about c, the ordinary particles having speeds close to c on the low side,
with tachions on the other side.
Again some limits can be obtained from pressure curves such as those
in Fig. 1, when they are continued to the left. A simple limit is given by
the threshold counters when they are set to count electrons: There are no
tachions to a limit of 10~ 3 of the pions. In at least one case (25 GeV/c
secondary momentum), the differential counter was set to count « on the
other side » up to velocities equivalent to « protons » : there were no counts
to a limit of 10~ 6 of the pions.
6*6. Longlived particles.  It would be rather difficult to detect a high
energy neutral particle with a lifetime longer than 10~ 6 sec and a relatively
small production crosssection [27]. The neutron is of such type, but is
abundantly produced. In analogy with the neutron detection method we
may speak of various detection methods for such objects:
a) by missingmass at production;
b) by interaction in various target materials; and
c) by activation and subsequent radioactivity.
New frontiers of highenergy physics 167
Let us consider, in particular, the last method. The delayed radioactivity
would be of the normal type if an excited nucleus is formed ; it would con
sist of highenergy particles if a type of hypernucleus would have been
formed. Such a delayed radioactivity, resulting in highenergy yrays and
electrons was searched for at CERN with negative results [28].
7.  Future perspectives.
As already stated, the present frontier of highenergy physics is repre
sented by the 76 GeV machine. Broadly speaking one can anticipate that
the accelerator will be used for:
a) the study of resonances in production experiments;
b) asymptotic behaviour, or better energy behaviour of crosssections;
c) systematic study of two body, quasitwobody, and manybody
processes;
d) neutrino physics;
e) searches for new phenomena, etc.
The 400 GeV Batavia accelerator and the 300 GeV European one will
probably follow the same lines.
Altogether new possibilities were opened up by the colliding beam ma
chines, though their small luminosities have until now precluded all but
the simplest measurements. The next generation of this type of accelerators
is starting now with the successful operation of the 1.5 GeV e+e~ ADONE
colliding beams of Frascati. Electronpositron colliding beams should, in
principle, allow a detailed study of many electromagnetic phenomena at small
distances, a precise investigation of the J PL = 1 boson resonances and so
on, while the CERN 25 GeV pp and the Novosibirsk 20 GeV pp colliding
beams should allow a first study of what is happening at much higher en
ergies. The program for the « first generation experiments » at the CERNISR
is now taking shape. It is not too different from the program at a new high
energy protonsynchrotron :
a) particle production;
b) total and elastic pp crosssections;
c) search for new phenomena, etc.
Increasing energies mean physically larger accelerators, bigger laboratories,
and much higher costs. Therefore it is clear that the number of superhigh
energy laboratories will be small, and that they will have an international
168 G. Giacomelli
character. Fortunately, highenergy physics has at present no strategic im
plication; so it is the field of science best suited for supranational cooperation.
Higherenergy conventional machines are becoming physically too large.
Several solutions to this problem may be envisaged:
a) the use of large superconducting magnetic fields;
b) colliding beam machines;
c) the development of completely new principles of particles accel
eration.
At the same time, one has to worry about particle beam optics at these
very high energies. Here, superconductors should be of great help in reducing
the dimensions of the beam elements ; superconducting RF cavities may allow
the separation of particles at much higher energies than at present.
As far as the possibility of doing experiments at such energies is con
cerned, the results of the CERNIHEP collaboration have shown that up
to 60 GeV/c the electronic separation of particles required only established,
though somewhat more refined, Cerenkov techniques, and did not pose any
major technical problem. The same techniques will probably be used for
the beams of higher energy machines. The counter beams of the future may
incorporate many long Cerenkov counters of different types. The timeof
flight technique will instead remain useful when searching for heavy mass
objects. The bubble chamber technique will still play an important role in
first surveys of what is happening, in particular for seeing new phenomena;
it will probably be used extensively to study neutrino interactions. Large
magnetic spark chamber spectrometers, and eventually total absorption spec
trometers of large dimensions, show prospects of becoming very important
types of detectors for the future accelerators. Cosmic rays may still allow
a glimpse at what is happening at much higher energies: do quarks really
exist? Will everything tend to energyindependent asymptotic limits? Will
the Pomeranchuck theorem be violated or will something new happen, such
as a new spectroscopy? Only accurate experiments at higher and higher
energies will give an answer to the questions.
I would like to express my thanks to all my colleagues [2, 13] of the first
collaborative experiments between the European Organization for Nuclear
Research and the Institute of HighEnergy Physics, Serpukhov. Most of
this note comes from their work and from discussions with them. I would
also like to thank all the people who made the collaboration possible, and
the members of the Directorate of IHEP for their hospitality.
New frontiers of highenergy physics 169
REFERENCES
[1] E. Amaldi: On the Dirac Magnetic Poles, Old and New Problems in Elementary Par
ticles (Academic Press, N. Y, 1968), p. 1.
[2] Yu. B. Bushnin, S. P. Denisov, S. V. Donskov, A. F. Dunaitsev, Yu. P. Gorin,
V. A. Kachanov, Yu. S. Khodirev, V. I. Kotov, V. M. Kutyin, A. I. Petrukhin,
Yu. D. Prokoshkin, E. A. Razuvaev, R. S. Shuvalov, D. A. Stoyanova, J. V. Al
LABY, F. BlNON, A. N. DlDDENS, P. DUTEIL, G. GlACOMELLI, R. MEUNIER, J.P. PeI
gneux, K. Schlupmann, M. Spighel, C. A. Stahlbrandt, J. P. Stroot and A. M.
Wetherell: Phys. Lett., 29 B, 48 (1969); Proc. Intern. Conf. Elementary Particles
(Lund, 1969) and Phys. Lett., 30 B, 506 (1969).
[3] M. Fidecaro, G. Finocchiaro, G. Gatti, G. Giacomelli, W. C. Middelkoop and
T. Yamagata: Nuovo Cimento, 24, 73 (1962).
[4] J. V. Allaby, F. Binon, A. N. Diddens, P. Duteil, A. Klovning, R. Meunier,
J.P. Peigneux, E. J. Sacharidis, K. Schlupmann, M. Spighel, J. P. Stroot, A. M.
Thorndike and A. M. Wetherell: paper submitted to Intern. Conf. HighEnergy
Physics (Vienna, 1968).
[5] D. G. Crabb, J. L. Day, A. D. Krisch, M. T. Lin, M. L. Marshak, J. G. Astbury,
L. G. Ratner and A. L. Read: Phys. Rev. Lett., 21, 830 (1968). J. L. Day, N. P.
Johnson, A. D. Krisch, M. L. Marshak, J. K. Randolph, P. Schmueser, G. J. Mar
mer and L. G. Ratner: to be published.
[6] R. Hagedorn and J. Ranft: Suppl. Nuovo Cimento, 6, 169 (1968).
[7] G. Cocconi, L. J. Koester and D. H. Perkins: Calculation of particle fluxes from pro
ton synchrotrons of energy 10 to 1000 GeV, in Proc. 200 GeV Summer Study (Aspen,
Colorado, 1967).
[8] G. Giacomelli: Total crosssection measurements, in Progress in Nuclear Physics
(Pergamon Press, Oxford, 1970), Vol. 12, pag. 77.
[9] I. Ia. Pomeranchuk: Sov. Phys. JETP, 3, 306 (1956); 7, 499 (1958).
[10] V. Barger: Rev. Mod. Phys., 40, 129 (1968); V. Barger, M. Olsson and D. D. Ree
der: Nucl. Phys., B5, 411 (1968).
[11] N. Cabibbo, L. Horwitz, J. J. Kokkedee and Y. Ne'eman: Nuovo Cimento, 45 A,
275 (1966); H. Cheng and T. T. Wu: Phys. Rev. Lett., 22, 1405 (1969).
[12] S. Frautschi and B. Margolis: Nuovo Cimento, 56 A, 1155 (1968); V. N. Gribov
and A. A. Migdal: Yadernaya Fisika, 8, 1213 (1968).
[13] J. V. Allaby, Yu. B. Bushnin, S. P. Denisov, A. N. Diddens, R. W. Dobinson,
S. V. Donskov, G. Giacomelli, Yu. P. Gorin, A. Klovning, A. I. Petrukhin,
Yu. D. Prokoshkin, R. S. Shuvalov, C. A. Stahlbrandt and D. A. Stoyanova:
Phys. Lett., 30 B, 500 (1969) and Yadernaya Fisika (to be published).
[14] G. G. Bzenogikh, A. Buyak, K. I. Iovchev, L. F. KiRiLLOVA, P. K. Markov, B. A.
Morozov, V. A. Nikitin, P. V. Nomokonov, M. G. Shafranova, V. A. Sviridov,
Truong Bien, V. I. Zayachki, N. K. Zhidkov, L. S. Zolin, S. B. Nurushev and
V. L. Solovianov: paper submitted to the Intern. Conf. Elementary Particles (Lund,
1969); Phys. Lett., 30 B, 274 (1969).
[15] F. Binon, S. P. Denisov, S. V. Donskov, P. Duteil, G. Giacomelli, Yu. P. Gorin,
V. A. Kachanov, V. M. Kutyin, J. P. Peigneux, A. I. Petrukhin, Yu. D. Pro
koshkin, E. A. Razuvaev, R. S. Shuvalov, D. A. Stoyanova and J. P. Stroot:
Phys. Lett., 31 B, 230 (1970).
170 G. Giacomelli
[16] J. V. Allaby, G. Bianchini, A. N. Diddens, R. W. Dobinson, R. W. Hartung,
E. Gygi, A. Klovning, D. H. Miller, E. J. Sacharidis, K. Schlupmann, F. Schnei
der, C. A. Stahlbrandt and A. M. Wetherell: Nuovo Cimento, to be published.
[17] Yu. M. Antipov, I. I. Karpov, V. P. Khromov, L. G. Landsberg, V. G. Lapshin,
A. A. Lebedev, A. G. Morosov, Yu. D. Prokoshkin, Yu. V. Rodnov, V. A. Ry
bakov, V. A. Rykalin, V. A. Senko, B. A. Utochkin, N. K. Vishnevsky, F. A. Yetch
and A. M. Zajtsev: Phys. Lett., 29 B, 245 (1969); and to be published.
[18] E. Lillethun: Nucleon reactions, in Proc. Intern. Conf. Elementary Particles (Lund,
1969).
[19] B. A. McCusker and I. Cairns: Phys. Rev. Lett., 23, 658 (1969).
[20] R. K. Adair and H. Kasha: Phys. Rev. Lett., 23, 1355 (1969).
[21] D. E. Dorfan, J. Eades, L. M. Lederman, W. Lee and C. C. Ting: Phys. Rev. Lett.,
14, 999 and 1003 (1965).
[22] Yu. D. Prokoshkin: seminar (1970).
[23] D. H. Perkins: Proc. 1969 Topical Conf. Weak Interactions (CERN 697, 1969), p. 1.
[24] R. Burns, G. Darnby, E. Hyman, L. M. Lederman, W. Lee, J. Rettberg and
J. Sunderland: Phys. Rev. Lett., 15, 830 (1965).
[25] P. J. Wandererer Jr., R. J. Stefanski, R. K. Adair, C. M. Ankenbrandt, H. Kasha,
R. C. Larsen, L. B. Leipuner and L. W. Smith: Phys. Rev. Lett., 23, 729 (1969).
[26] O. M. Bilaniuk and E. C. G. Sudarshan: Phys. Today, 22, 43 (1969).
[27] M. Pontecorvo: 1969 Seminar at IHEP.
[28] M. Fidecaro, G. Finocchiaro and G. Giacomelli: Nuovo Cimento, 22, 657 (1961) L.
The K°K° System in pp Annihilation at Rest.
M. GOLDHABER
Brookhaven National Laboratory  Upton, N. Y. (*)
C. N. Yang
Institute for Theoretical Physics, State University of New York  Stony Brook, N. Y. (**)
In the annihilation of stopped p by p, neutral K meson pairs are produced
in ~10 2 of the events. This K°K° system is of a very special nature [1]
and it seems worthwhile in the light of the discovery of CP nonconservation
to discuss [2] what one can learn from a more detailed study of this system.
The discussion is perhaps especially relevant since in the not too distant
future it should become possible to stop a sufficient number of antiprotons
in hydrogen in a welldefined geometry [3] to pursue statistically significant
experiments concerning the system.
In the reaction
(1) p+p > K°+K°+ neutrals ,
for fixed momenta P 1 and P 2 of the two K's, there are four states: \SS>,
\SL}, \LS}, and \LL) where the first (or second) letter denotes the short or
long lived nature of the K with momentum P 1 (or P 2 ). Assuming CPT in
variance, but not separate C, P, or T invariance, one has [4], with suitable
normalization,
(2)  \K s )=p\Ky + q\K),
\ \K£>=p\K>q\K>.
It follows that
(3a) \SS} + \LL) = 2p*\KK} + 2q 2 \KK} (forbidden)
(36) \SL> + \LS} = 2p*\KK>  2q*\RK> (forbidden)
(*) Supported by the U. S. Atomic Energy Commission.
(**) Partially supported by the U. S. Atomic Energy Commission under Contract
No. AT(30l)3668 B.
172 M. Goldhaber and C. N. Yang
and
(4a) \SS} — \LL> = 2pq\KK) + 2pq\KK} (allowed, parity = + 1)
(4b) \LS> — \SL} = 2pq\KK> — 2pq\KK)> (allowed, parity = — 1)
The two states (3a, b) are forbidden by strangeness conservation. The indi
cated parity of the two states (4a, b) is the intrinsic parity of the two K's
taken as a single system in the final state of (1).
1.  Experiments requiring the detection of one K°.
It follows from (4) that in pp annihilation one has an incoherent source
of K s and JL L with an intensity ratio of I to 1, if one confines oneself to
the observation of only one neutral K decay. (It seems to us difficult to ar
range for another source of this type.) One has thus a rather direct method
for measuring the decay rates of K s into 7r+7r~7r°, 7i 7r°7i°, 7T"(ji+v, 7r+fjirv, 7rre+v
or Tu+e~v. (These rates have so far not been experimentally measured. Com
parison of the rates of K 8 ^niv and Ki>7i;(v yields, of course, direct
information on the AQ =£ AS question.) The sum total rate of these decays
is expected to be ~ 10~ 3 that of K s >7r + rc _ . The spatial distribution of the
point of decay of K s ^'7z + n~, which is readly measurable, should be the
same as that of any other K s decay mode. This allows for a simple method
to separate out the K L decay modes (which form the main background events)
from the K s decay modes under study. Scattering of the K s and K^ before
decay can introduce uncertainties in the experiment. The amount of matter
between the target and the detector is therefore best minimized.
In pp annihilation, detection of a charge asymmetry in the decay
K L ^niv would be a direct proof of CP violation, independent of the usual
theoretical analysis of the time dependence of the K°K° complex, since the
initial particles producing the K L (i.e. pp) are their own CP conjugates.
(In contrast, the usual charge asymmetry experiments [5] examine K L pro
duced in hadronic collisions not involving antinuclei. They therefore demon
strate CP violation only if one accepts the analysis that the K L observed are
the same whether they are produced in CP selfconjugate collisions or not.
While this analysis is in all probability correct, there is an explicit advantage [6]
in a direct experimental demonstration of the important phenomena of CP
violation without having to use such an analysis.) The experiment can only
be successful, however, if one observes — 10 7 or more K^ decays.
The K°K° system in pp annihilation at rest
173
2.  Experiments requiring the detection of two K°'s.
The decay amplitudes of the two states (4a) and (4b) are tabulated in
Table I, for the case when the AQ = AS rule holds. The Table requires
minor modifications if AQ = — AS is also allowed. The notations used in
Table I are as follows:
£?i = exp [—  ?l s n + /Am n] , ^ t = exp [— \l L h] ,
Am = m L —m s = 0.469 2. s , where A s = decay rate of K s ,
r}=rj + _, \rj + _\ 2 = 3.7xl0~ 6 ,
ja 2 = 6.6xl0 4 ; \p\ 2 oo \q\ 2 = ,
Table I.  Decay rate into various modes at t x and t 2 . It is assumed that the AQ = AS
rule holds (*).
Decay
h
*2
Amplitude of LSSL
t:\l + v
7T+TC 
paiSe^n^i^)
TTpl^V
tt+t:
qa^^+v^J?,)
7T+TT 
~ + 7T~
^(=^1^2 —^1=^2)
TU[X + V
TT[X+V
^« 2 (^1^ 2 ^1^ 2 )
7TX~V
7T[i.~V
 9 2 «*(^1^ 2 ^1^ 2 )
Ufl+V
Tr[x _ v
paga^^^+Sr !^)
7T+7C 
TCfi+V
painse^STiSe*)
Amplitude of SSLL
paiSf^r,^^)
qa^^ + r]^^)
(.sr^rfse^
— Ij a \Cr jt7 2 — =* 1 =* 2)
(*) For explanation of notation used in Table, see text.
if 7T ev is considered instead of 7C(jlv, a 2 increases by a factor of 1.34. For
those cases where the decay products at t 1 and t 2 are the same, such as
(Tv + 7i~) ti (Tz + T~) t2 , each observed event should count as  event at t ly t 2 and \
event at t 2 , t x . The amplitudes are normalized such that, e.g., the probability
of the state 2~*[S , ,S> — \LV)\ to decay into (k\l + v) at t x and (ti+tt  ) at f 2 * s
\\pa(Sf x y 2 — r} r £ x Sfa^CAfdfxdfaXf). The factor (AJd^dfgXf) are common to
all decay modes. Notice that decay into (7T[jl + v) at t 2 and (71+tt  ) at t x is a
separate entry in the Table.
A traditional type of experiment in which one concentrates on events
with no final pions:
pp^SL or SS
174 M. Goldhaber and C. N. Yang
has led to the conclusion that there are few, if any, events of type (4a).
(This result is to be expected [7] if the pp annihilation occurs in the S state,
resulting in total parity equal to — 1.) Improved statistics for this type of
experiment would be useful.
Observation of the interference of \LS} states with \SL} states, or of
\SS) with \LL), in the mode (71:^)^(71+71:)^ would lead to a measurement [8]
of both the absolute value and the phase of rj + _ , as is obvious from Table I.
For this experiment, the two K's could be produced together with pions.
Even so, intensity is a severe problem, and it is doubtful that the experiment
could be successful with less than 10 11 K pairs, or 10 13 stopped p.
The KK system should exhibit especially interesting properties if CPT
invariance should be violated. Such a violation cannot be discussed at pre
sent at any fundamental level, since no model violating CPT invariance can
be constructed that satisfies the requirements of Lorentz invariance and
minimum analyticity. However, one could discuss the possibility that the
usual decay formalism still holds phenomenologically, with the two eigen
modes \K s y and \K L } in eq. (2) given instead by
(5) J \Ka>=p'\K> + q'\K>,
In such a case the two states with zero strangeness are, instead of (4a) and (4b) :
(6a) \SS>?£ \LL} + \ g J) QLS} + \SL» =
= i(fP^W (ja> + K>)>
(6b) \LSy\SL} = (pq'+ qp >)(\KKy\KKy) .
Equation (6a) exhibits the possibility of observing an interference between
\SSy and \LS} term , which is present only when
(7) q  P  = 2(S^Q,
q p
implying violation of CPT invariance. To search for such an interference
it is probably best to look for the decay (tcCv) at t x togetehr with the decay
(7T+7T  ) at t 2 from a single pp annihilation. The probability of such events
depends on t x and t x as follows:
(8) exp [V 2 ]exp [— \(l 8 — 2i Am) t x ] +£exp [— lX L t x ]\ 2 .
The K°K° system in pp annihilation at rest 175
The interference term would yield a measurement of fi. To appreciate the
difficulties of the experiment let us assume that ^~2xl0~ 3 . The most
bothersome background is then due to the decay of (6b) into the same state
with time dependence:
(9) ~ exp [— A s t 2 ] exp [— 1 L t x ] .
While the time dependence on t x can serve to separate (9) from (8), the small
magnitude of ft makes the separation possible only with enormous statistics.
It is doubtful that the experiment could be done with fewer than 10 n K
pairs or 10 13 stopped p. On the other hand, if CPT invariance should be
violated, the essential parameter ft seems measurable only in an experiment
of this type.
REFERENCES
[1] Previous discussions of this topic can be found in M. Goldhaber, T. D. Lee and
C. N. Yang: Phys. Rev., 112, 1796 (1958); and ref. [7].
[2] For a previous analysis see V. L. Lyuboshitz, E. O. Oknov and M. I. Podgoret
skii: Sov. J. Nucl. Phys., 6, 907 (1968).
[3] From a practical point of view it may be desirable, in order to enrich the sample with
K°K° events, to surround the hydrogen target with anticoincidence counters. To ob
serve K s decays high precision is needed, such as is already obtainable with streamer
chambers. To observe K L decays, very large volume detectors would be needed.
[4] T. D. Lee, R. Oehme and C. N. Yang: Phys. Rev., 106, 340 (1957).
[5] See review in Proc. Vienna Conf. on HighEnergy Phys. (1968).
[6] See, e.g., C. N. Yang: Brookhaven Lecture (October 1965) in Brookhaven National
Laboratory Lectures, vol. 3 (New York, 1965).
[7] B. d'Espagnat: Nuovo Cimento, 20, 1217 (1961); M. Schwartz: Phys. Rev. Lett.,
6, 556 (1961); G A. Snow: Phys. Lett., 1, 213 (1962); R. Armenteros et ah: Proc. of
CERN Conf. on HighEnergy Physics (1962).
[8] Unlike a number of experiments under progress on the phase angle of r) + _ which suffer
somewhat from a lack of knowledge of the precise K°K° composition, this approach
is free of such problems.
Symmetry Principles in Physics.
T. D. Lee
Columbia University  New York, N. Y.
1.  Introduction.
Symmetry considerations have played an important role since the beginning
of physics. A great deal of our understanding of nature can be formulated
through symmetry principles. However, especially over the past decade, we
have learned that many of these symmetry considerations turn out to be not
strictly correct. Why do natural laws have a connection with symmetries;
but often with a slight amount of asymmetry rather than with perfect sym
metry? For example, physical laws are almost symmetrical with respect to
left and right. However, in the weak interactions where
weak forces 6
strong forces
the rightleft symmetry is broken. Similar symmetry breaking effects have
been observed for many other trasformations ; these are summarized in
Table I.
Table I.  Symmetry violations in strong interaction processes (e.g., np^np).
Violation amplitude
Symmetry (relative magnitude)
P (space inversion) 10~ 6
C (particle antiparticle conjugation) 10~ 3  10 6
T (time reversal) 10" 3  lO" 15
CP 10 3  10" 15
SU 2 (isospin) 10" 2
su, 10 1
Symmetry principles in physics 111
This situation may appear to some people as aesthetically disturbing.
Why should nature be slightly asymmetrical?
Before starting the technical discussion of these symmetries and asym
metries in physics, let us recall that the word « symmetry » has two different
meanings even in our daily language. According to the 1949 Webster's
Dictionary (*), these two definitions are:
syrn'metry (sfm'£.trf), n. [F. or L.; F. symmStrie (now symStrie),
fr. L., fr. Gr. symmetria, fr. syn + metron a measure.] 1. Now
Rare. Due or balanced proportions; beauty of form arising from such
harmony. 2. Correspondence in size, shape, and relative position, of
parts that are on opposite sides of a dividing line or median plane.
It is of interest to note the italic Now Rare for the first definition. Can it be
anticipating the broken symmetry principles that physicists have now dis
covered about nature? Indeed, as we shall see, perhaps beauty should be
associated with a slight asymmetry, rather than with total symmetry.
The concept of beauty is, of course, quite subjective. Which is a more
beautiful object, one with total symmetry, or one with a slight asymmetry?
The answer is clearly open to debate. However, we may take a look at some
of the wellknown art pieces. For example, both the Greek statue and the
mosaic from S. Apollinare in Classe near Ravenna, shown in Figs. 1 and 2,
emphasize bilateral symmetry. The painting of Poplars by Monet in Fig. 3
suggests a discrete spacetranslational symmetry. While the beauty of sym
metry is clearly demonstrated in each case, this beauty is greatly enhanced
by the presence of slight asymmetries.
In physics, our concern is with the laws of nature. The concept « beauty »
comes in only because of our belief that nature is beautiful. The concepts
« symmetry » and « asymmetry » are applied to the various transformations
which are connected with both spacetime coordinates and the interactions
between elementary particles. Both symmetry and asymmetry should be
formulated in terms of precise mathematical language, so that their impli
cations can lead to predictions which can be tested experimentally.
There are four main groups of symmetries, or broken symmetries, that
are found to be of importance in physics.
1) Permutation symmetry: BoseEinstein and FermiDirac statistics,
2) continuous spacetime transformations: translations, rotations, accel
erations, etc.,
(*) Webster's New Collegiate Dictionary, 1949 edition (G. and C. Merriam Co.,
Springfield).
12
178
F. D. Lee
Fig. I.  Praying Boy, Greek sculpture. Reprinted lYcm H, WtYL: Symmetry
{Princeton University Press, Princeton, New Jersey, 1952).
Symmetry principles in physics 179
Fig. 2,  Mosaic from S. Apollinarc in Clas.sc.
Fig. 3.  Poplars by Claude Monet (on display at the Metropolitan Museum of Art).
180 T. D. Lee
3) discrete transformations : space inversion P, time reversal T, particle
antiparticle conjugation C, Gparity, etc.,
4) unitary transformations:
t/ r symmetries : conservation laws of charge Q, baryon number N,
and lepton numbers L e and L^, SU 2 (isospin) symmetry, and SU 3 sym
metry.
Among these, the symmetries connected with the first two groups of transfor
mations are, at present, believed to be exact. In the third group only the
product CPT is perhaps exact, but each individual discrete symmetry oper
ation is not. In the fourth group only the t/ r symmetries are exact.
2.  Symmetries, nonmeasurables and conservation laws.
The root af all symmetry principles in physics lies in the assumption that
it is impossible to measure certain basic quantities; these will be called non
measurables in the following discussion. For example, we may consider the
interaction energy V between two particles at positions r x and r 2 . The physical
assumption that it is not possible to measure an absolute position leads to
the mathematical conclusion that the interaction energy V should be un
changed under a space translation
and
Therefore, the interaction energy V is a function only of the relative distance
0"l— r 2)» *'•*•>
(1) V=V(r 1 rJ.
From this, we deduce that the total momentum of this system of two par
ticles must be conserved, since its rate of change is equal to
_(V 1 + V a )K
which, due to (1), is zero.
This simple example illustrates the close connection between three aspects
of a symmetry principle: the assumption of a nonmeasurable, the implied
invariance under the connected mathematical transformation and the physical
consequence of a conservation law. In an entirely similar way, we assume
Symmetry principles in physics 181
absolute time to be a nonmeasurable ; the physical laws must then be invariant
under a time translation
t>t + r
which results in the conservation law of energy. By assuming absolute direc
tion to be a nonmeasurable, we derive rotation invariance and obtain the
conservation law of angular momentum.
Similar reasoning extends to all other symmetry considerations. The
special theory of relativity assumes that absolute velocity is a nonmeasurable,
and the general theory of relativity assumes that the difference between an
acceleration and a gravitational field is not a measurable quantity. The
permutation symmetry rests on the impossibility of observing any difference
between identical particles.
In order to derive the conservation law of electric charge, we assume that
it is not possible to measure the relative phase between states of different
charges; therefore, one must have invariance under an arbitrary multiplica
tion of phase factor e id between states of different charges. Since e id is a
simple lxl unitary matrix, this invariance is called « L^symmetry ». It im
plies that the transition matrix elements between states of different charges
must be zero, for otherwise there could be interference between two states
of different charges, and their relative phase would be measurable. This
E/jsymmetry then leads to the wellknown conservation law of electric charge.
Similarly, the impossibility of measuring relative phases between states of
different baryon numbers implies the conservation of baryon number; the
assumption that relative phases between states of different lepton numbers
are nonmeasurables results in the conservation of lepton number.
3.  Symmetry violations.
Violations of symmetries arise when what were thought to be non
measurables turn out to be actually measurable. Let us take as a first example
the question of rightleft symmetry.
The concept that nature (i.e., physical law) is symmetrical with respect to
right and left dates back to the early history of physics. Of course, in our
daily life left and right are quite distinct from each other. Our hearts, for
example, are usually on our left sides. The word « right » means also correct,
while the word <•< sinister » in its Latin root means left. In English, one says
rightleft, but in Chinese, j£ (left) always precedes fa (right). However,
182 T. D. Lee
such asymmetry in daily life is attributed to either the accidental asymmetry
of our environment or the initial condition in organic life.
The principle of the symmetry between right and left has been found to
be true in classical physics, in atomic physics, and in many areas of nuclear
physics. Yet, in 1957 it was discovered that the laws of nature are in fact not
symmetrical with respect to right and left. The apparent symmetry previously
found in macroscopic physics, atomic physics, and nuclear physics is only
an approximate one. For example, the neutrino emitted in a 7r+ decay has
its spin always antiparallel to its momentum. Although the initial iz + , being
of zero spin, is in a totally spherically symmetrical state, nevertheless we may
use its final decay product to give an absolute definition of left versus right,
The same applies to other violations of symmetries. Previously, in electro
magnetic theory, the sign of electric charge could only be defined in terms of
that of a test charge. Now, because of C and CP asymmetries, one may give
an absolute definition of the sign of electric charge. For example, in the
decay of the longlived neutral K meson, K^,, the decay rates [1, 2] to e+ and [i+
are different from those to e~ and yr:
rate (K° r > e + 7rv )
, ; * ^= 1.003 15 ±0.0003
rate (K" > e~7r; + v e )
and
rate(K°^ [ i.7i+v (i )
Such slight differences in decay rates enable one to give an absolute definition
of the sign of electric charge, without the use of a test charge.
As discussed in the previous Section, the validity of all symmetry principles
rests on the theoretical hypotheses of nonmeasurables. Some of these hy
potheses may indeed be correct in a fundamental sense, some may simply be
due to the limitations in our present abilities to measure things. As we improve
our experimental techniques, our domain of observations naturally becomes
enlarged. It should not be too surprising that we may even succeed in ob
serving some of those supposedly nonmeasurables, and therein lies the root
of symmetry breaking.
In this sense, we should be prepared for the eventual possibility that we
might be able to measure absolute spacetime positions, absolute direction,
and absolute velocity, and even relative phases between states of different
charges, different baryon numbers, and different lepton numbers. Even if
these were possible, it should be expected that such discoveries could lead
only to small symmetry breakings in all of the presently known physical
Symmetry principles in physics 183
phenomena, because, otherwise, these supposedly nonmeasurables would have
been measured long ago.
Just as in most of our artistic creations, the harmony and beauty of sym
metry is always enhanced by the presence of a small degree of asymmetry.
From an aesthetic point of view, it is rather satisfying to find nature also has
a similar preference in small symmetry violations.
REFERENCES
[1] J. Steinberger: Proc. CERN Topical Conf. Weak Interactions (1969), p. 291.
[2] D. Dorfan et ah: Phys. Rev. Lett., 19, 987 (1967).
The Design and Use of Large Electron Synchrotrons.
A. W. Merrison
Daresbury Nuclear Physics Laboratory  Daresbury, U. K. (*)
1.  Introduction.
The large proton synchrotrons built in the last 20 years have been hugely
successful in their contributions to knowledge in elementary particle physics.
This has been due primarily to the fact that they serve as intense sources of
secondary particles in the giga electronvolt region.
The contribution of the large electron accelerators has not, until recently,
been anything like as striking as that of the proton accelerators, but now
that many electron accelerators are working in the giga electronvolt range
this is a situation which has changed, and is changing, rapidly. It is very
clear that the large electron accelerators can be used to investigate phenomena
in a way quite complementary to the proton accelerators.
There is a fundamental peak energy limitation for large cyclic accelerators,
first pointed out by Iwanenko and Pomeranchuk which, while quite unim
portant for proton accelerators, is critical to the building of electron accel
erators. This is the classical electromagnetic radiation emitted by a charge
undergoing acceleration — in the case of an accelerator, the centripetal accel
eration caused by the charged particle following a curved orbit. It can easily
be shown that the energy loss Ai? (in MeV) of a charged particle of energy
E (in MeV) in one complete orbit of a circle of radius R (in meters) is given by
AE
An e 2 1 E \ 4
where e is its charge and m its rest mass. For electrons this reduces to
A£=8.84xl0 14 ^.
R
(*) Present address: University of Bristol, Bristol, U.K.
The design and use of large electron synchrotrons 185
As a practical example, the 5 GeV electron synchrotron NINA has a
bending radius of 21 m which leads to an energy loss at the maximum energy
of 2.6 Me V/re volution. But since this radiation loss occurs inversely as the
fourth power of the rest mass it is completely negligible for all practicable
proton accelerators.
It can be shown also that if the magnetic guide field varies sinusoidally
with time, which is usually the case with electron synchrotrons, then the
mean energy loss (in watts) W through synchrotron radiation, if the mean
accelerated current of electrons is / (in amperes), is given by
FF= 5.78x10*^,
jR 2
where / is the repetition frequency in cycles/sec. This shows clearly that
where the synchrotron radiation is a serious consideration it can be reduced
by increasing the repetition frequency of the synchrotron and its radius.
Apart from the difficulty of providing sufficient radiofrequency power to
overcome this loss and then to accelerate the electrons, a more fundamental
limitation is created by this socalled synchrotron radiation. Since the elec
tron loses energy not continuously but by the discrete emission of photons,
synchrotron oscillations are created which can lead to serious difficulties with
the available magnet aperture for practical accelerators. However, for the
accelerators discussed in this paper this is not likely to be a serious limita
tion, and schemes to reduce it have been put forward by, for example,
Robinson.
Of course, none of these considerations applies to linear accelerators and
this is why the largest electron accelerator built so far, the 20 GeV accelerator
at Stanford, is a linear machine. Such accelerators, since they are not cyclic,
suffer the serious disadvantage that their duty cycle is very short; in the case
of SLAC, for example, it is 0.05 % . This limits the class of experiment which
can be carried out with this kind of accelerator, though it is entirely possible
that this difficulty will be overcome by the current development of super
conducting radiofrequency cavities. This limitation in turn has concentrated
a great deal of study on the possibility of building large electron synchro
trons, which have the virtue of a good duty cycle.
2.  What is the maximum practicable energy of an electron synchrotron»
This question has been discussed in some detail by CrowleyMilling [1]
and some of his simple arguments will be presented.
We can get an absolute limit to the maximum energy in a synchrotron
186 A. W. Merrison
of given configuration by setting the radiated energy loss per revolution equal
to the energy gain per revolution.
In a conventional synchrotron the perimeter is made up of guide fields,
where the radius of curvature of the electrons is R, and straight sections
which contain other ancillary equipment — such as, for example, the accel
erating cavities — leading to a « mean radius » r for the synchrotron. The
maximum energy gain per revolution is given by
(*)■
(1) A2s G = 2nrer I 1 J k cos y ,
where s is the maximum electric accelerating field, r is the transit time factor,
k is the fraction of total straight length available for acceleration, and (p is
the synchronous phase angle. By setting this equal to the synchrotron radia
tion loss at peak energy and using practicable values for the parameters in (1)
of t = 1, Rjr = 0.6, k = 0.8, cos 99 = 0.7 and e = 1 Mv/m we arrive at the
peak energy E
E = 1.78 xlOM.
Again as a practical example for r = 1.2 km (which is the radius of the
proposed European 300 GeV proton synchrotron) we have E = 62 GeV.
Another limitation discussed by CrowleyMilling is that given by the fact
that the radiofrequency losses in the normally conducting structures usually
used as radiofrequency accelerators increase rapidly as the energy increases.
If we say that the electric field required to maintain the particles in acceler
ation varies as E* then clearly the radiofrequency power required to setup
these fields will vary as E 8 . Again by making reasonable assumptions about
the overall accelerator structure the dependence of the maximum energy on
available radiofrequency power can be deduced.
If one assumes that it would not be unreasonable to use 10 MW of radio
frequency power in such an accelerator the peak energy from an electron
synchrotron with parameters similar to those used above (including a mean
radius of 1.2 km) will be about 45 GeV. Since most of this power would
still be absorbed in the accelerating structure, beam loading would not be
a serious problem and it looks feasible to accelerate mean currents of up
to 10 [aA.
3.  The Daresbury « Booster ».
For some time now a certain amount of study has been given to the
possibility of using the 5 GeV electron synchrotron NINA as the injector
to a very much larger synchrotron in the (15^20) GeV range [2]. This was
The design and use of large electron synchrotrons
187
prompted by a number of considerations: the clear need in the future for
a long dutycycle accelerator in this energy range ; the high cost of the injector
for such a machine; and the fact that the topology of the Daresbury site is
well suited to the construction of the main accelerating ring of the large radius
required if the radiofrequency power is to be kept within acceptable limits.
By the time the electrons in NINA have been accelerated to 2 to 3 GeV,
the emittance and energy spread of the beam are very small and this means
Scale
Fig. 1.  Layout of Daresbury site for the NINA Booster.
tunneling.
represent
188 A. W. Merrison
that the magnet aperture of the main accelerator (the « Booster ») can be
made correspondingly small. Again even with a large radius, the high injec
tion energy means that the magnetic field in the main ring at injection can be
very high. Since in this case much larger remanent and eddy current fields
can be tolerated at injection this in turn means that one can contemplate
quite simple forms of construction for the vacuum chamber.
One possible layout which has been studied for the NINA Booster is that
shown in Fig. 1. This particular layout has the advantage of making the
maximum possible use of the experimental facilities, including the existing
NINA experimental hall, on the Daresbury site. It can be seen too from this
layout how much of the main ring would lie in a tunnel through the hillside
on which NINA has been built.
The general form of the booster would be that of a superperiod machine
with 4 « quadrants » each on a mean radius of about 1 50 m with long straight
sections, each of 100 m, separating them. Two of these straight sections
would be sufficient to house the radiofrequency accelerating sections required
for acceleration to 20 GeV. A list of the leading parameters is given in
Table I.
Table I.
Parameter Units
Peak energy 15/20 GeV
Mean current 1/3 uA
Mean radius 146.9 m
Bending radius 120.0 m
Magnetic field on equilibrium orbit (20 GeV) 0.56 T
Length of full magnet 7.25 m
Total number of full magnets 104
Betatron oscillations per turn 17.75
Length of straight section 100.0 m
Magnet excitation frequency 53 Hz
Radiation loss/turn 20 GeV 118 MeV
15 GeV 38 MeV
Radio frequency power (mean) at 15 GeV, 1 [xA 95 kW
It seems quite clear that there are no real problems in building a quite
conventional synchrotron to accelerate the NINA beam to 15 GeV with
perhaps 1 \lA (mean) of accelerated electrons. Before embarking on a second
stage which would take 3 jxA, say, to 20 GeV it is certain that the possibility
The design and use of large electron synchrotrons 1 89
of superconducting radiofrequency structures must be investigated thoroughly.
The preliminary cost estimates of the first stage are £ 3.82 million, with an
additional £ 0.7 million required for the second stage.
4.  Experimental use of a 70 GeV electron synchrotron.
It is important to bear in mind in thinking about possible experiments
for a high energy electron synchrotron that for the most part they will be
experiments which it will be impossible to do with a proton synchrotron of
comparable or higher energy. There are certain experiments which would be
done on either kind of accelerator and for which the electron machine will
offer certain advantages, but these form rather a special class.
As an illustration of this one can look at the secondary particle yields
worked out by P. G. Murphy [3] for the NINA Booster at 20 GeV with
3 [iA of accelerated electrons and compare them with the CERN PS. In all
cases the Booster yields are a factor of between 2 and 5 down on those from the
CERN PS. But there are situations where it would be more advantageous to
use the Booster secondary particle beams. Longlived neutral kaons, for
example, are much more free (by a factor of 10 or more) from neutron con
tamination, and in addition because of the high radiofrequency used in the
booster (816 or 1224 MHz) timing information on the kaons can be obtained.
It must be emphasised however that the principal experiments to be done
with high energy electron synchrotrons will certainly be those using electrons
or photons as the primary particle.
A number of specific experiments which can be done with (15f20) GeV
electrons are investigated in some detail in the report referred to by Murphy
and Clegg [3]. They have confined their attention to experiments where
a good duty cycle is essential or, at the least, very desirable. Since the photon
has a unique combination of quantum numbers (spin, helicity, C) no rest
mass and a relatively weak interaction there are many experimental situations
where the photon is an ideal tool to use as the primary particle. This is par
ticularly the case when one studies the vector mesons which, leaving aside
the mass, are rather « photonlike » in their properties. The success of the
vector dominance model in the strong interaction does not need underlining.
In the same sense, in inelastic electron scattering experiments, the electron
can be looked on as a source of « massive » virtual photons. But it is quite
clear that all such investigations will call for complicated coincidence exper
iments and will depend on a long duty cycle accelerator for exploration in
depth. The field however is extraordinarily rich and can be approached only
with an accelerator of the kind discussed in this paper.
190 A. W. Merrison
REFERENCES
[1] M. C. CrowleyMilling : Daresbury Technical Memorandum EL/TM/43 (1966).
[2] M. C. CrowleyMilling and A. W. Merrison: Daresbury Technical Memorandum
EL/TM/49 (1967); and Daresbury Report DNPL/R2 Preliminary design study for a
1520 GeV electron synchrotron: NINA Booster.
[3] P. G. Murphy and A. B. Clegg (eds.): Daresbury Report DNPL/R3 Experimental
utilization of a NINA Booster (1969).
Breaking of the SU 3 x SU Z Symmetry in Hadronic Physics.
L. Michel
Inst it ut des Hautes Etudes Scientifiques  BuressurYvette
L. A. Radicati
Scuola Normale Superiore  Pisa
1.  Introduction.
In this paper we analyze the properties of the three fundamental inter
actions (strong, electromagnetic, and weak) from the point of view of the
SU 3 xSU 3 group. For this analysis we will use an extension of the geometrical
approach which we have introduced before [1, 2] for SU 3 . In that case the
three charges conserved by each interaction namely the hypercharge Y, the
hadronic electric charge Q H , and the weak hypercharge Z, are generators
of the unitary linear representation of SU 3 on the Hilbert space of hadronic
states. That is, in the representation a ~> Q{a) e if(^) of the SU 3 Lie algebra
on 3t, Q H , Y, Z are the images of three vectors — q, y, z of R 8 , the octet space,
i.e., the eightdimensional real vector space of the Lie algebra of SU 3 . As
we have shown in ref. [1] the isotropy groups of these vectors are maximal
subgroups of SU 3 and the vectors themselves are solutions of a nonlinear
equation.
It is however clear that for a full understanding of the properties of the
interactions and of their relations we need to consider the group SU 3 x SU 3 .
Indeed the different behavior under space reflections of the three inter
actions, cannot be described in terms of the diagonal SU 3 subgroup alone.
We will see that some of the interesting geometrical properties of the
vectors y, q, z can be carried over to SU 3 xSU 3 . We will show that the
directions along which the symmetry group is broken are, also in this case,
solutions of nonlinear equations of the type postulated by the bootstrap
approach to symmetry breaking.
Two subgroups of SU 3 x SU 3 are of special significance for hadron physics :
SU 3 and SU 2 xSU 2 . Both represent approximate invariances of the strong
192 L. Michel and L. A. Radicati
interactions which are valid when one neglects either the difference between
the K and Tcmeson mass (for SU 3 ) or the pion mass (for SU 2 xSU 2 ).
Recently GellMann, Oakes and Renner [3] have suggested that the strong
Hamiltonian which breaks the SU 3 x SU 3 symmetry transforms approximately
like an element of the (3, 3) © (3, 3) representation which is left invariant
by SU 2 xSU 2 . We will show that in the space of the (3, 3) © (3, 3) repre
sentation we can define two directions which are solutions of nonlinear
equations and whose isotropy groups are precisely SU 3 and SU 2 xSU 2 .
In Sect. 2 after a brief resume of the relevant results of refs. [1] and [2]
we will discuss the unique symmetrical algebra, on the space of the (1, 8)©
© (8, 1) and of the (3, 3) © (3, 3) representations, which have SU 3 x SU 3 as a
group of automorphism. The existence on these spaces of symmetrical
algebras insures the possibility of having nonlinear equations whose so
lutions define the directions along which SU 3 xSU 3 is broken.
2.  Mathematical preliminares.
2'1. Geometry of the octet.  We begin by briefly reviewing a coordinate
free formulation [1] of the SU 3 invariant algebras on the octet space R 8 .
We can realize R 8 as the real vector space of all 3x3 Hermitian trace
less matrices a, b, c, .... Any element u of the group SU 3 is the form u =
= exp [— icpajl], aeR 8 . The action of SU 3 on R 8 (which is the space of its
adjoint representation) is
(1) a ^> uau* = uaur 1 .
We can define on R 8 an SC/ginvariant scalar product and two algebras
which have SU 3 as automorphism group:
Scalar product:
(2) (a, b) = \trab
SU 3 Lie algebra:
(3) af\b= l [a,b}.
Symmetrical algebra:
(4) a yb = \{ab + ba)  f (a, b) = \{a, b]  f (a, b) .
If a and a \Ja are linearly independent they generate a twoplane ^ a {ie. a two
dimensional subspace of R 8 ) which is a Cartan subalgebra {i.e. a maximal
Abelian subalgebra) of the SU 3 Lie algebra. Thus ^ a which is isomorphic
Breaking of the SU 3 xSU 3 symmetry in hadronic physics 193
to U x x U x is the Lie algebra of the isotropy group (or little group) of a.
If on the contrary
(5) qWq + fj(q)q = 0,
the isotropy group is a U 2 group which we denote by U 2 (q) . Any vector whose
isotropy group is a U 2 will be called a « q vector ». From now on we will
consider only normalized « positive » q vectors, i.e. such that: (q, q)=l,
fj(q)> 0. This implies, rj(q) = 1/V3
The Cartan subalgebras of the SU 3 Lie algebra are all conjugate (i.e.
transformed into each other) by the SU 3 group. One of them is of course
made with the diagonal matrices ueSU 3 . It can be proved that any <$
contains three positive normalized # vectors at 120° from each other. Conv
ersely if jcjgR 8 commute, ax + /?y and a'x + fi'y commute, and generate
a ^ (denoted ^x,y)' For positive normalized ^vectors we thus have
(6) (qi,qd= — io#A# = and qt¥qj.
Given a ^vector y, the vectors t y of U 2 (y) which are orthogonal to y form
the SU 2 (y) subalgebra of U 2 (y). They satisfy the following relations:
(7) y/\t y = y/\t' y = Q\ CM) = CM') = 0; V%\fty = (h,t y )y.
The normalized t a of the three ^vectors of a Cartan subalgebra <€ form
the hexagon of the « roots » different from zero.
2'2. The SU 3 X SU 3 algebra.  To extend this formalism to SU 3 X SU 3 we
consider the space R 16 = R 8 © R 8 . We call a + and a_ the elements of the
first and the second R 8 , respectively (the index ± corresponds in physics
to the chirality) and denote by a = a + © a_ an element of R 16 . The Lie
algebra of SU Z x SU 3 is then defined by
(8) a A I = (a+ © a_) A (b + © fe_) = (a + A 6 + ) © («_ A 6_) ,
where A in the righthand side has been defined on R 8 in eq. (3). The scalar
product invariant under SU 3 x SU 3 is the CartanKilling form which we write
(9) (a + ®a_,b + ® b_) = K«+ , K) + Kfl , *) •
It is also convenient to use another decomposition of R 16 into a direct
sum R 8 © R 8 . In this decomposition, which is symbolically illustrated in
Fig. 1, we denote the element a = a + ®a_ by (a\a') with
(10) a + =a\a' and a_= a — a'.
13
194 L. Michel and L. A. Radicati
sut'
antidiagonal
Fig. 1.  Decomposition of R 16 into a direct sum of R 8 ff)R 8 .
In this notation the Lie algebra law (6) becomes
(11) aAb = (a\a')A(b\b') = (aAb + a'Ab'\aAb' + a'Ab)
and the scalar product
(12) {a,l) = {a,b) + {a\b').
In a similar way we can extend to R 16 the symmetrical algebra on R 8 :
(13) aVb = (a\a')\/(b\b') = (a\jb^ r a'yb'\a\/b'+a l \jb) .
One verifies that the equation
(14) a\/a = Xa,
has only two types of solutions:
05) a=(q\0)
and
(16) a=(q\±q),
where q is a ^vector.
The subalgebra of SU 3 x SU 3 which leaves invariant (i.e. commutes with)
a ^vector (j0) of the diagonal SU 3 subalgebra is the set of all (««') such
that yAa = 0, yAa' = 0; it will be denoted (U 2 \U 2 ) y . With the notation of
(8) it is the direct sum U ( 2 +) (y) © U 2 \y) .
Breaking of the SU 3 xSU 3 symmetry in hadronic physics 195
2'3. The (3, 3) (3, 3) representation.  A special role in the physical
applications is played by the (3, 3) representation of the group or of the
Lie algebra SU 3 x SU 3 . We can realize the 9dimensional space of this repre
sentation as the complex vector space of the 3x3 matrices m. Under the
transformation u + xu_= exp [— i<pa + /2] x exp [— iya_/2], m goes over into :
(17) /w~> u + mu* .
The representation of the Lie algebra is thus
( 1 8) D(a) m = D(a + a_)m = — l(a + m — ma_) ,
or
(19) D(a)m = D(a\a')m = —~([a, m] + {a', m}) .
(Equation (18) is obtained from (17) by differentation with respect to <p,
at cp = 0.)
The representation is unitary for the group, i.e. it leaves invariant the
Hermitian scalar product
(20) <!»! , m 2 > =  tr {ml m 2 ) .
The 9dimensional complex vector space C 3 ^ can be considered as an
18dimensional real vector space R 18 . The 1 8dimensional representation of
the group SU S x SU 3 on this space is the direct sum of the (3, 3) and its complex
conjugate (3, 3). It is real and unitary, hence orthogonal. It leaves invariant
a Euclidean (i.e. real orthogonal) scalar product which is the real part of
(20), while the imaginary part becomes an antisymmetrical real (i.e. sympletic)
scalar product. Explicitely we have:
(21) 0»i,»2) = Re<m 1 ,w 2 > = Itrt/wfma + /nm 1 ) ,
(22) )m 1 , m 2 ( = Im (m 1 , w 2 > = — tr (m\m 2 — mtm^ .
Any 3x3 complex matrix can be written in the form
(23) m = Vul + m + iVf 1//'+ im' = (ji\m\\fj,'\m') ,
where ju and fx' are real members and m and m' are vectors of the octet space.
In this notation (21), (22), and (23) read
(24) (m 1 , m 2 ) = /x lf x 2 + ju[ju' 2 + (m lt m 2 ) + (m' x , m 2 ) ,
(25) )m x ,m 2 ( = fx^ 2 — ^ 2 + (m l9 m 2 ) — (m[, m 2 ) ,
196
L. Michel and L. A. Radicati
and eq. (19) reads
(26) D{a\a')(jj\m\\fi'\m') =
= (Vf(a', m')\aAm + a'ym' + V//a' — V}(a\ m)\a/\m r —a'\/m — V$fjia') .
Tensor operators which represent physical observable must be Hermitian
on Jt. It is therefore necessary that they belong to a real representation
of the invariance group. This is the case of the (3, 3) © (3, 3) representa
tion which, we want to emphasize, is irreducible as a real representation.
The tensor product of (3, 3) © (3, 3) by itself when decomposed into
real irreducible representations contains the (3, 3) © (3, 3) once.
Hence from two vectors r, s e (3, 3) © (3, 3) it is possible to form a new
vector of the same representation which we denote r T s. The symbol T is
the law of a symmetrical algebra on R 18 which has SU 3 x SU 3 as automorphism
group. By standard methods we find
(27) r T s = l l(trr* trs*— tr (r*s*)) — §#•* trs* — \s* tr r* + {r*, s*} .
We leave to the reader to check that
(28)
D(a\a')r T s = (D(a\a')r) T s + r T (D(a\a')s) ,
which means that SU 3 xSU 3 is a derivation algebra of the ^product.
With the notation (23) we can write eq. (27) in the form
(29)
where
and
(30)
r r J = (TfT'f'),
r = (^ro'r') and s = (o\s\\o'\s')
r = =(2QO2 Q 'o'(r, s) + (r f , s')) ,
t = —^{—os — or + q's' '+o' 'r')\r\Js — r'\ls'
\/6
t' = ~(qs'+ q's + o'r + or') — rys'— r'\js
Breaking of the SU 3 xSU 3 symmetry in hadronic physics 197
We add two more properties of this product
( 31 ) <x T y, z> =<x,y T z> ,
(32) <*, x T x} = f detx = (x T x, x) + i)x T x, x( .
The (3, 3) © (3, 3) representation of SU 3 x SU 3 has no invariant for the sub
group (U 2 \U 2 )y, i.e. if for all (a\a')e(U 2 xU 2 ) y , D(a\a')m = eq. (26)
shows that m = 0. However if a' is restricted to be in SU 2 (y), the same equa
tion shows the existence of a twodimensional invariant subspace spanned
by the vectors
(33) (v\V2ny\W\V2n'y),
where y is a ^vector and r\, r\' are real numbers. We will denote the isotropy
group (or its Lie algebra) of the vectors (33) by (U 2 (y)\SU 2 (y)). This Lie al
gebra is the following direct sum
(34) (U 2 (y)\SU 2 (y)) = SUpty) © SU^iy) © U*(y) ,
where Uf(y) = (Ux(y)\0) is the Lie algebra generated by (y\0) (see Fig. 1).
The vectors (33) have an interesting property under the Tproduct. Let
y((p) be the vector (33) with
(35) tj =V^coscp , rj' = VJ sin^ .
These vectors are normalized
( 36 > 0#),J#)> = 1.
They belong to the SU 3 xSU 3 orbit oi>(0) and satisfy the quadratic equation
(37) yQp) T y(<p , ) = o.
Moreover one shows that all unit vectors of R 18 satisfying such an equation
are on the SU 3 x SU 3 orbit of y(0).
Equation (37) is a particular case of the equation
(38) m T m = Am .
If I =£ (and m ^ 0) one also shows that the only unit vectors which are
solutions of (38) are on the two orbits of ±n=± V2/3 1 which are SU$
invariants. The unit vectors which have SU$ as isotropy group form a circle
(39) 11(99) = Vf exp [i(p]l = (cos<p0sin<p0)
n{cp ±n)= — n((p)
198 L, Michel and L. A. Radicati
and they generate the Tsubalgebra
(40) <<P) T <<P') = ^ln(cpcp>) .
3.  Geometrical properties of the three interactions.
3*1. The SU 3 symmetry.  We begin by recalling the basic properties of
the interactions under the SU 3 group, i.e., the diagonal subgroup SUf of
sui +) xsui\
a) The hypercharge Y and the three isospin operators T 1 ,T 2 ,T 3 =
— Q H + \ Y generate the invariance group U 2 (y) of the strong interactions.
The extension of this invariance to SU 3 implies considering U 2 (y) as a sub
group of SU 3 . This means that y is a q vector of which Y is the image in the
representation of the SU Z algebra in the Hilbert space Jf of hadron physics.
The electric hadronic charge Q H is the corresponding image of — q and
the relation Q n =T z \\Y implies that q is a # vector. The SU 2 (q) group is
called the « [/spin group ».
b) According to Cabibbo's hypothesis the two charged components of
the vector current v± coupled to the leptons and the electromagnetic cur
rent j e  m ' belong to the same SU$ octet. We denote by c 1= bz'c 2 the directions,
of y±. Using the additional property that the electric charges of v± are ± 1
we can deduce
(41) y/Zci V c 1 = V3c 2 V c 2 = z ,
where z is a ^vector. The operator Z, which is the image of z, is the weak
hypercharge conserved in weak interactions.
The vector z commutes with q but not with y. We thus have in R 8 two
distinct algebras ^ ay and %> qz which have q in common. The noncommuni
cativity of y and z reflects the existence of strangeness violating weak inter
actions. As one can see from (6) the difference from 0° or 120° of the angle
between y and z gives a measure of the noncommunicativity of Y and Z
and is therefore related to the Cabibbo angle 6. Explicitely we have
(42) (j,z)=lfsin 2 0.
It can be proved that two noncommuting gvectors y and z uniquely define
another ^vector which commutes with both of them. This vector is given
by the relation
(43) q = ((y, z) \)\<fiy\/z + \{y + z)) .
Breaking of the SU 3 xSU 3 symmetry in hadronic physics 199
Thus the strong and weak interactions determine uniquely the direction
of the electromagnetic interactions.
Cabibbo has also postulated that the axial currents af belong to another
SU% octet in the same directions c 1= b/c 2 as v±. The two assumptions about
the vector and the axial vector currents are in good agreement with experiment.
3'2. SU 3 xSU 3 symmetry.  Since the weak interactions have a definite
(negative) chirality whereas the electromagnetic and strong interactions have
a defined parity, their relations can only be fully understood by considering
the enlarged group SU 3 xSU 3 . It has indeed been suggested [3, 4] that this
group and its subgroups provide a reasonably approximate frame for the
study of hadron physics. Cabibbo's hypothesis can be generalized to SU 3 x SU Z
by assuming that j* m ; v± , a± belong to the same representation of this group
namely the adjoint representation (8, 1) 0(1, 8). We can thus write for the
currents :
(44) #». = h£q\0) ; v± = ^(c±0) ; fl ± = ^(0c±) .
The weak currents are thus
(45) /z± = ^(c±c±).
As Q H is the integral over space of the time component of j e  m , the integrals
(46) Q(a\a') = (d 3 x h (a\a') ,
are at a given time the generators of SU 3 xSU 3 . We shall now list the co va
riance properties of the three interactions under SU 3 x SU 3 :
a) The isotropy group of the electromagnetic current hj^q\t$\ and
therefore of the electromagnetic interactions (see Sect. 2*2) is (U 2 \U 2 )q =
= Ui + \q)®Ui\q).
b) The pair of weak currents hjic^ — c±) and therefore the semi
leptonic weak interactions have for isotropy group SU^ U[~\z).
c) The co variance of the CP conserving Hamiltonian M ? NL for non
leptonic weak interactions is not yet established. If it involves only charged
currents as many physicists would prefer [5] then it would have components
outside the (1, 8)0(8, 1) representation. It is however compatible with the
present evidence to assume that ^ NL belongs entirely to the representations
(1, 8)0(8, 1) in the direction (z\—z) [6]. If this were the case the isotropy
group of M" NL would be SU 3 +) © U^~\z) which is a maximal subgroup of
SU 3 xSU 3 . Nothing is known for the CP violating part.
200 L. Michel and L. A. Radicati
d) We have said that U 2 (y) and SU$ are approximate invariances of
the strong interactions. Another interesting approximate invariance has been
recently proposed by GellMann, Oakes, and Renner [3]. According to
them, in the limit where the pion mass can be neglected the strong Hamilto
nian is of the form
(47) jf s = jr + jr(/ft),
where J^ is invariant under SU 3 xSU 3 and 3^{ni) transforms like the
(3, 3) © (3, 3) representations. They also suggested that to a good approxi
mation m coincides with the vector y(0) of eq. (37).
In this model the approximate isotropy group of the strong interactions
would be (U 2 \SU 2 ) y which is a maximal isotropy group for the nonzero vector
of the (3, 3) © (3, 3) representation.
Even though the mass difference m K — m n is larger than m n , SU 3 remains
an interesting approximation for the strong interactions. The SU 3 xSU 3
breaking part in eq. (47) is in the SU 3 invariant direction denoted by «(0)
in eq. (39). It is remarkable that its isotropy group (SU$) is the other max
imal isotropy group of the nonzero vectors of the (3, 3) © (3, 3) represen
tation.
3'3. SU 3 xSU 3 and space reflections.  In the limit where they are exact
the U 2 (y) and SU§ symmetries of the strong interactions commute with the
Poincare group (without time reflection).
For the exact SU 3 x SU 3 symmetry the invariance group is no longer a
direct product of the internal symmetry group by the Poincare group but
the following semidirect product
(^ x^x^))xZ 2)
where ^ is the connected Poincare group and the nontrivial element r of Z 2
acts on ^ like the space inversion and interchanges SU^ with SU^ +) . The
action of r on the (8, 1) © (8, 1) representation is
(48) (a\a')^(a\—a').
This allows to assign a parity to the elements of the (8, 1)0(1,8) repre
sentation; the primed vectors have odd parity, the unprimed ones have
even parity.
For the (3, 3) © (3, 3) representation, eq. (26) shows that the primed
and unprimed quantities which appear in (23) have opposite parity. For
example j(0) and y(7t/2) (see eq. (33)) are eigenvectors of r with opposite
parity. As we have seen, SU 3 x SU 3 implies the existence for this represen
Breaking of the SU 3 xSU 3 symmetry in hadronic physics 201
tation of the Talgebra and this fixes in the SU 3 limit the assignment of the
parity. Indeed, as we have shown, the direction along which SU 3 xSU 3 is
broken in an St/ginvariant way satisfies the nonlinear equation
(49) n(0) T n(0) = ]/ «(0) = n^j T n (^j .
Thus under r
(50) m = (ji\m\\fi'\m') ^(ji\m\\—iA , \—m'') .
4.  Remarks on symmetry breaking.
It has been suggested by several authors [7] that the SU 3 or the SU 3 x SU 3
symmetries are spontaneously broken. Such a symmetry breaking occurs
when the invariance group K of a stable state of a physical theory is only a
subgroup of the invariance group G of the theory itself. In this case all
states of the same orbit GJK of solutions are all stable states.
We have shown [1, 8] that in a theory based on a variational principle
spontaneous symmetry breaking can occur and one expects the subgroup K
to be a maximal isotropy group among those of all possible orbits. As we
have seen the breaking of SU 3 x SU 3 by the strong interactions has the above
property both in the SU 3 or in the SU 2 x SU 2 approximation [9]. The same
is true of Jt NL if its invariance group is SU^ +) @U^~\z) (see Sect. 3'2). This
may therefore suggest that the SU 3 xSU 3 symmetry of the hadronic world
is spontaneously broken by the strong and perhaps also the weak inter
actions.
The intersection between the two isotropy groups of the weak nonleptonic
nteractions and of the strong interactions in the GellMann, Oakes, and
iRenner model is:
(51) (SU^ © Ui\z)) n (SUi + \y) ® SUtXy) tf?G0) = SUf\y) £/<"%) ,
where q is a ^vector commuting with y and z which, as we have seen, is
uniquely defined once y and z are fixed. The intersection of the two groups
in the lefthand side of (51) and SUi is Uf(q) which is thus the only invariance
group for the interactions between hadrons (when the hadronlepton inter
actions are disregarded) and corresponds to the conservation of the electro
magnetic charge. We have thus the following scheme of decreasing inva
riance inside the hadronic world
O (U 9 \SU a )y d
SU 3 XSU 3 UMDU^q).
o SUi 1
202 L. Michel and L. A. Radicati
Let us remark that the isotropy group of the electromagnetic Hamiltonian
is (U 2 \U 2 ) q . This group is not maximal in SU 3 xSU 3 for the (1, 8) ©(8, 1)
representation.
However the direction (q\0) of the electromagnetic interactions shares
with the directions of the two other interactions, i.e. (z\—z) and y(0) or
«(0) the following properties: they are the different types of solutions of
SU 3 xSU 3 invariant nonlinear equations:
(52) (a\a')v(a\a , ) = A(a\a f ),
for (q\0) and (zz);
(53) m T m — lm ,
for the two directions along which SU 3 xSU 3 is broken with approximate
SU 3 or SU 2 invariance. Bootstrap approaches to symmetry breaking lead to
this quadratic type of nonlinear equations.
It is interesting to note that for an SU 3 x SU 3 invariant theory, the space
inversion operator r can only be denned modulo an inner SU 3 xSU 3 auto
morphism. However, as we have discussed in Sect. 3'3, the existence of the
Talgebra fixes naturally the parity of the vectors of the (3, 3) © (3, 3) rep
resentation of SU 3 x SU 3 and the vector w(0) has even parity. Thus the
requirement that the breaking due to strong interactions satisfies eq. (53)
fixes the parity of the hadronic states.
It is also worthwhile to point out that one of the solutions of eq. (52),
(z— z) has a pure chirality corresponding to maximal violation of the
parity fixed by the strong interaction. The other solution (q\0) has a definite
parity and its direction q is fixed when j(0) and (z— z) are known. From
the point of view of SU 3 x SU 3 the three directions according to which the
symmetry is broken have thus fairly simple properties and correspond to
all three types of solutions of the nonlinear equations (52) and (53).
There is nothing however to tell us why the directions y and z should
make precisely the angle that is experimentally observed.
We do not want to discuss here the attempts [10, 11] to calculate 6. We
only remark that in the SU 3 xSU 3 scheme, m and (z— z) are not in the
same representation space. Thus an SU 3 x SU 3 invariant depending on these
two vectors has to be at least quadratic in m. For example if we define the
vector (see eq. (18))
v = D(z\ — z\i
z)m
we can form an SU 3 x SU 3 invariant <«, v} which is a function of (y, z).
Breaking of the SU 3 x SU 3 symmetry in hadronic physics 203
However the length of the vectors has not been given here a physical mean
ing as we did not take into consideration the strength of the coupling.
On the other hand a projective invariant such as f z = (jv T , v) (v, v}~$
depends upon both 6 and the matrix elements of m which are functions of
the physical masses. We note that in the limit where m = j(0) (invariant
under (U 2 \SU 2 )y, f z vanishes.
REFERENCES
[1] L. Michel and L. A. Radicati: Proc. Coral Gables Conference, 1968.
[2] L. Michel and L. A. Radicati: The geometry of the octet (unpublished).
[3] M. GellMann, R. J. Oakes and B. Renner: Phys. Rev., 175, 2195 (1968).
[4] For a review of the validity of the SU 3 x SU 3 symmetry and for an extensive list of
references see S. Weinberg: Proc. 14th Intern. Conf. HighEnergy Phys. (Vienna, 1968).
[5] M. Suzuki: Phys. Rev., 144, 1154 (1966); H. Sugawara: Phys. Rev. Lett., 15, 810
(1965); M. Suzuki: Phys. Rev. Lett., 15, 896 (1965). See also N. Cabibbo: Proc.
13th Intern. Conf. HighEnergy Phys. (Berkeley, 1967).
[6] L. A. Radicati: in Old and New Problems in Elementary Particles Physics, edited by
G. Puppi, p. 272 (Academic Press, New York, 1968).
[7] For a general discussion see R. E. Cutkowsky: Brandeis University Summer Institute
in Theoretical Physics, New York, 1965. The spontaneous breaking of SU 3 has been
specifically discussed by T. Nagy: Nuovo Cimento, 43 A, 654 (1966); R. Brout: Nuovo
Cimento, 46 A, 932 (1967); N. Cabibbo: in Old and New Problems in Elementary Par
ticle Physics, edited by G. Puppi, p. 62 (Academic Press, New York, 1968); L. Michel
and L. A. Radicati (see ref. [1]).
[8] L. Michel: in Lectures on Theoretical Physics, 10, 263 (1968), edited by W. E. Brit
ten and A. O. Barut.
[9] This property has been shown on an explicit model in the case of a SU 2 x SU 2 inva
riant mass term by G. Cicogna, F. Strocchi and R. Vergara Caffarelli: Phys.
Rev. Lett., 22, 497 (1969).
[10] R. Gatto, G. Sartori and M. Tonin: Phys. Lett., 28 B, 128 (1968) and Proc. CERN
Conf Weak Interaction (January 1969), p. 465.
[11] N. Cabibbo and L. Maiani: Phys. Lett., 28 B, 131 (1968) and Proc. CERN Conf
Weak Interaction (January 1969), p. 485.
Structure of Matter Investigations
by Thermal Neutrons in Rome.
A. Paoletti and S. Sciuti
Comitato Nazionale per VEnergia Nuclear e (CNEN)  Roma
Istituto Fisico della Facoltd di Ingegneria  Roma
1.  Introduction.
As it is well known, the slowing down of neutrons and the interacting
properties of thermal neutrons with matter were discovered in Rome by
Amaldi, Fermi, Pontecorvo, Rasetti and Segre [1] thirtyfive years ago.
Since then a tremendous amount of work has been done in all the world
in the field of nuclear, atomic and molecular physics by means of thermal
neutrons which at the present time are still successfully employed in many
first class investigations.
Until 1955 there was very little in nuclear energy researches going on
in Italy; particularly in the field of the socalled « pile neutron research »
every thing was to be started « exnovo ».
E. Amaldi had always followed with great interest this kind of research
and was convinced of the necessity of promoting it in Italy also. Among
the several lines of research with neutrons he suggested neutron diffraction
for solid state investigations warmly promoting also the use of thermal
neutrons in nuclear physics.
This point of view was completely accepted by the Comitato Nazionale
per le Ricerche Nucleari [2] leading to the constitution of the Laboratorio
di Fisica Nucleare Applicata in Rome and of similar units in other Italian
nuclear Centers [3].
In this paper we would like to briefly describe some recent research both
in nuclear and solid state physics carried out at the Casaccia Center of CNEN,
Rome, using thermal neutrons.
The thermal neutrons are provided by the 1 MW, RC1 reactor [4]. Two
radial beam tubes are employed for solid state physics work, while two
tangential beam tubes, one completely crossing the biological shield, are
used for nuclear physics experiments.
Structure of matter investigations by thermal neutrons in Rome
205
2.  Nuclear physics work.
The (n, y) reactions are intensively used at the Casaccia Center to study
nuclear levels in different classes of nuclei. Besides these experiments we
would like to describe one which makes use of a very fruitful technique
developed in our laboratory [5]. High energy gammalines (5^8) MeV pro
duced from (n, y) reactions in a target located very close to the reactor core,
come from a beam tube completely opaque to neutrons and impinge on a
scatterer which is viewed by Ge(Li) and Nal(Tl) large detectors. When a
gammaline resonantly excites a high energy level of the target (scatterer)
nucleus, a gammaray cascade takes place originating an inelastic scattering
process. In this way the physical characteristics of the high energy level
starting the cascade, together with the lower ones populated by the cascade
can be efficiently studied analysing the high resolution single spectra, the
angular distributions, the coincidence spectra, etc.
In Fig. 1 a sketch of the experimental setup [6] is shown. In general
this technique allows one to study several nuclear parameters such as resonant
crosssections, ground state and total radiation widths [7], and finally to
determine the level scheme of nuclei restricted to the transitions starting
j fn.fiSOUBer "
Fig. 1.  Nuclear spectroscopy work at the RC1 Reactor: The experimental
setup concerning resonant scattering.
from the resonant level. This kind of spectroscopy gives information similar
to those obtainable with (n, y) reactions with the advantage that level spins
can be determined by measuring the directional correlations of the elastic
and inelastic gammarays; further (y, y') reactions are the most suited for
206
A. Paoletti and S. Sciuti
the study of stable isotopes which may not be reached by (n, y) reactions.
The choice of the target is considerably restricted by the requirement that a
random overlap should exist between the incident gammaline and a level
in the particular nuclide to be studied.
Nevertheless about 50 cases of nuclear resonance fluorescence, almost
near the closedshell regions, have been since observed [8].
We have systematically studied ten nuclei by the nuclear resonant tech
nique [7]. Of these the level scheme of 62 Ni, 112 Cd, 118 Sn [6], 205 T1 and 65 Cu [9]
have been deduced.
An example of the power of the method in spectroscopy work is given
in Fig. 2. Monocromatic photons (7646 keV) produced by Fe(n, y) reaction,
resonantly excite a 205 T1 level. The analysis of all the spectrum shows the
existence of more than 20 levels with energies between ground state and
~3.5MeV. In the figure a portion of inelastically scattered gammarays,
detected by a 30 cc Ge(Li) counter, is reported.
COUNTS
den 50907 KeV
/^4rWHM e 17KeV
d*04899KeV
■
1
'""■'•■ ' 'Wi%\.
d«D5333 KeV t "'^^f
dec54855KeV
WWk'
wL
de.p. 5347KeV s«.p. 4925 KeV
3.90
4.000
4.100
4200
4300 4400
4.500
E r (KeV)
COUNTS
P5425.6 > Hi «925KeV
iTWHM* 16 KeV
d e.p.5 773Kf
8.P5333* 5347KeV
4mS side
Ej CKeV)
Fig. 2.  Nuclear spectroscopy work at the RC1 Reactor: A portion of the
(inelastic) spectrum of 205 T1 resonantly excited by Fe(n, y) 7 646 keV yline.
In conclusion we would like to point out that nuclear spectroscopy by
gammarays resonant scattering excitation leads to results very similar to
that achieved by Coulomb excitation and therefore it may be considered a
very important part of a research program to be performed with reactors.
Structure of matter investigations by thermal neutrons in Rome 207
3.  Solid state physics work.
Neutron diffraction is a powerful tool for studying some microscopic prop
erties of solids such as magnetic structures, magnetization densities, lattice
dynamics, magnetic excitations, phase transitions, etc.
At the Laboratorio di Fisica Nucleare Applicata research has been per
formed in ferromagnetism by use of the polarized neutrons. The static and
dynamic behaviour of unpaired electrons in metals and alloys has been
investigated mostly by determining magnetization density maps and disper
sion relations of spin waves. So far neutron diffraction has been used at
Casaccia mostly for 3d electrons [10]; however recently experiments have
been carried out also on Ad and 5d electrons.
Transition metals of Ad or 5 d group do not exhibit a magnetically ordered
state as elements, but some of their alloys with 3d metals show bulk mag
netization properties which were interpreted as indicating a contribution of Ad
and 5d electrons to magnetization. Polarized neutrons provide an unique
tool for obtaining direct microscopic information and have been successfully
used both for elastic and inelastic scattering from some Pt alloys, namely
CoPt 3 , CoPt, and MnPt 3 [11]. It has been possible to ascertain that a fairly
welllocalized magnetic moment of about 0.2 Bohr magnetons is generally
present on Pt atoms, and magnetization density maps have indicated the
spatial distribution of 5d electrons and the symmetry of their wave functions.
These results are appreciably affected by the interaction with neighbour
atoms as it is proved by their dependence on the order parameter. A typical
magnetization density around a Pt site in a MnPt 3 alloy with order parameter
S = 0.22, is given in Fig. 3. One notices that:
1) The magnetization changes from negative to positive values going
from the center of the site outward.
2) The distribution of unpaired electrons is highly aspherical.
The first result can be consistently interpreted by assuming that the moment
of Mn atoms occupying the Pt site, because of the incomplete order are
directed opposite to bulk magnetization. Their negative magnetization due
to 3d electrons which are fairly concentrated prevails around the nucleus while
the positive magnetization of 5 d electrons which are more spread out is prev
alent away from the nucleus. (One must remember that neutron diffraction
provides information on the single sites of the unit cell but averaged over
all the unit cells of the sample.)
MnPt 3 has been also investigated from the dynamical point of view. The
acoustical branch of the spin waves dispersion curve has been determined
208 A. Paoletti and S. Sciuti
[001]
0.02
Fig. 3.  Neutron diffraction work at the RC1 Reactor: Threedimensional
magnetization map around the Pt site in a MnPt 3 alloy.
with polarized neutrons by the « diffraction method », which provides such
information with a simple two crystals experiment. The results have been
interpreted according to calculations performed at Casaccia [12] on alloys
of Cu 3 Au type and provided the values for the MnPt and MnMn exchange
integral in fair agreement with estimations based on the Ising model.
Structure of matter investigations by thermal neutrons in Rome 209
REFERENCES
[1] E. Amaldi, E. Fermi, B. Pontecorvo, F. Rasetti and E. Segre: Ric. Scient.,5 (2), 380
(1934). For more details on this subject see: The production and slowing down of neu
trons. E. Amaldi: in Encyclopedia of Physics, Vol. XXXVIII/2; S. Flugge (1959).
[2] Now Comitato Nazionale per PEnergia Nucleare (CNEN).
[3] See for instance: G. Caglioti: Notiziario CNEN, 11, 44 (1968).
[4] L. Di Palo, G. Focaccia, E. Lo Prato, F. Marsili, A. Paoletti, M. Perni, D. Pro
spers S. Sciuti and A. Verri: Energia Nucleare, 14, 659 (1967).
[5] M. Giannini, P. Oliva, D. Prosperi and S. Sciuti: Nucl. Phys., 65, 344 (1965).
[6] R. Cesareo, M. Giannini, P. Oliva, D. Prosperi and M. C. Ramorino: Nucl. Phys.,
A 132, 512 (1969).
[7] D. Prosperi and S. Sciuti: Suppl. Nuovo Cimento, 5, 1265 (1967).
[8] G. BenDavid, B. Arad, J. Balderman and Y. Schlesinger: Phys. Rev., 146, 852
(1966).
[9] R. Cesareo, M. Giannini, P. Oliva, D. Prosperi and M. C. Ramorino: Results
presented at the Int. Symp. on Neutron Capture GammaRays, August 1115, Stud
svik (1969).
[10] For a full bibliography of the work at Casaccia on the subject until 1966, see Noti
ziario CNEN, May 1966, p. 85.
[11] F. Menzinger and A. Paoletti: Phys. Rev., 143, 365 (1966); B. Antonini, F. Men
zinger and A. Paoletti: Phys. Lett., 25 A, 372 (1967); B. Antonini, F. Lucari,
F. Menzinger and A. Paoletti: Phys. Rev., 187, 611 (1969); B. Antonini, M. Felici
and F. Menzinger: Phys. Lett., 30 A, 310 (1969).
[12] F. Leoni and C. Natoli: Nuovo Cimento, 55 B, 21 (1968).
14
Search for New Stable Particles.
B. PONTECORVO
Joint Institute for Nuclear Research  Moscow
1.  Introduction.
Everybody knows the extraordinary contribution which Edoardo Amaldi
has given to the development of modern physics, from Xray to molecular
physics, from his classical neutron investigations to problems of nuclear
techniques etc., not to speak of his great merits in forming young scientists
and, last but not least, in organizing modern physics in Italy (and not only
in Italy!).
As a rule the research work of Amaldi is fundamental and quantitative
in character, a fact which is evident also in all his first class numerous books
and review articles, and yet he occasionally likes to perform brave, qualitative
experiments whose significance is going together with a very small a priori
probability of finding a positive result (for example, the search for magnetic
monopoles, or several unpublished old time experiments « a porte chiuse »
performed in Rome). For this reason I would like to dedicate the present
paper to my friend Edoardo, with whom my first steps in science are closely
connected, in the hope that he will not form a too severe judgement of this
extremely naive piece of fantasy.
In modern accelerators, to the development of which Amaldi is devoting
much of his time, the available collision energy is steadily increasing, so that
the question naturally arises among physicists as to whether there might
not exist unknown and entirely unpredictable « stable particles » which are
produced in such accelerators.
Here stable particles are defined as objects with a mean life >l(h 8 s;
as it will be explained below, the figure 1(H s is arbitrary and corresponds
simply to the shortest available pulse of accelerated protons in modern
machines.
There has already been performed a number of experiments in order to
search for new stable particles [1 ]. All the relevant investigations and proposals
Search for new stable particles 211
made up till now are characterized by the following circumstances:
a) the search is made for electrically charged particles,
b) for the identification of such particles a beam well resolved in
momentum is analyzed and various quantities (momentum, ionization, time
of flight, ...) are measured without the decay properties of the new particles
being investigated.
Below, a method is proposed for the search of both neutral and charged
« stable » particles. The advantage of a method which may be operative for
neutral as well as for charged particles is immediately evident if one keeps
in mind that among the known particles the number of neutral objects is
about equal to the number of charged ones.
In order to discover the new particles it is proposed to study their radio
activity properties with the help of a special method.
2.  The idea of the experiment.
There are reasons to assume as a working hypothesis that new particles
with mean lives > 1CH s might exist, that is that the transformation of such
particles into lighter particles is strongly forbidden in some way. As an
illustration we could think, for example, that the decay of the new particle
is due to the second order weak interaction in G, the Fermi constant being
G = 10 5 /Mp 2 . Then the probability of decay will be 1/t & G 4 £ 9 , where E
is a certain energy characteristic of the process. If, for example, the Hhyperon
had a mass < 1115 MeV, instead of 1315 MeV, its mean life could be longer
than hours! Besides, the existence of a hyper on with strangeness — 2 and
mass < 1115 MeV might lead to the appearance of long living quasinuclei
(a sort of hypernuclei) with special properties and, in particular, to a new
form of radioactivity of matter, in which the decay energy is not measured
in million electronvolts but is of the order of 100 MeV. However, I wish to
stress again that this example is only an illustration and the possibility that
the metastability of the new particles, if they really exist, is to be found out
side the boundaries of the known physics seems to me much more plausible.
Such metastability might be related to the existence of yet unknown quantum
numbers, or to something else, for example, to an unusual combination of
known quantum numbers [2].
Generally speaking, the body of information accumulated in the region
of atomic and nuclear physics tells us that metastability is a property appearing
in the most various phenomena, from phosphorescence to nuclear isomery,
from the existence of strange particles to the decay K + ^ 7r + +7t°, etc.
212 B. Pont e cor vo
I am just proposing to use electronic methods for the search of a new
type of high energy radioactivity, related to the existence of particles which,
due to a forbidity of unknown nature, decay with a very long mean life
(> 10" 8 s). Below, the assumption will be made that these new particles
are strongly scattered by nucleons. As to the production mechanism of such
particles, there will not be made any hypothesis.
3.  How to detect the new particles?
I shall illustrate here the case when the new particles are electrically neutral.
Then the discovery of the neutron and of its properties tells us how it is pos
sible, in principle, to detect new neutral particles. As it is well known, neu
trons may be detected in many ways:
1) There are detected nuclear recoils in elastic collisions of fast neutrons
with nuclei (especially protons). Such a method is not adequate for the dis
covery of new particles, because their flux is expected to be very small, so that
the number of nuclear recoils due to the new particles is negligible in com
parison with the number of recoils produced by neutrons.
2) Nuclear reactions produced by fast neutron bombardment with the
emission, for example, of protons, alphaparticles, etc., are looked for. Such
a method is also inadequate for detecting new particles, because their flux
is very small.
3) There are observed nuclear reactions (n, y), (n, p), (n, a), fission, etc.
produced by neutrons after they have been slowed down. The possibility
of slowing down new particles is not to be excluded, but since such particles
are expected to be generated with an energy of several 10 10 eV, the slowing
down process requires very large dimensions of moderator (a fact which
greatly complicates the detection of the new particles, whose intensity is
very small at best). Under certain circumstances, however, (see below) slowing
down of new particles could be used.
4) There are observed radioactive properties of the neutron (generally
speaking, of the nucleon). Today the observation of the free neutron decay
is not a difficult problem; however, it is necessary to have a very intense
neutron beam to observe the decay of free neutrons. The detection of the
decay of the new particles in their free state is a very unpractical proposition,
especially if their mean life exceeds 10 7 s. But the detection of neutrons
turns out to be quite effective if the decay of bound neutrons (that is if the
beta radioactivity induced by neutron bombardment) is looked for. The
Search for new stable particles 213
analogy for new particles would be the search for a special type of radio
activity of pseudonuclei, that is of quasinuclei within which the new particle
is found together with ordinary nucleons (I do not call these quasinuclei
« hypernuclei », because by definition hypernuclei are A quasinuclei : hyper
nuclei cannot have a mean life much longer than 10~ 10 s).
It is natural to expect that the new particle (probably produced together
with other particles) in high energy collisions of protons or y quanta with
nuclei, as a rule will leave the original nucleus and then will be « stopped »,
either suddenly (after a few collisions) or gradually after slowing down by
many collisions. For such « stopping » of the new particles a large amount
of condensed matter is required; I will not discuss here the corresponding
experiments and I shall note that only radiochemistry, which permits the
separation of « pure » source of quasinuclei from a large amount of irradiated
material may give positive results (if the lifetime is long enough).
Below, however, I shall consider the relatively rare but experimentally
favourable possibility that in a proton or photon collision with a nucleus a
new particle is produced, which is trapped « at the place of birth » (that is,
which is found eventually inside the nucleus product of spallation); in such
a circumstance, a radioactive quasinucleus, analogous to a hypernucleus,
will be produced. Of course this requires that the new particle is being strongly
scattered (and attracted) by nucleons. Thus the experiment, which will be
discussed below, consists in the search for a new type of « radioactivity »
(with mean life > 10 8 s) in a target, irradiated in a very high energy
accelerator, the radioactivity being notable for the high energy of its decay
products (hundreds of million electronvolts instead of million electronvolts
as in the ordinary radioactivity).
Immediately there arises the question: What limits on the production
crosssection of such particles can be obtained from experiments already
performed ? If the mean life of the new particles is less than a few days, there
are no limits for the crosssection, because to the best of my knowledge no
relevant experiments have been performed. Some limits on production cross
sections, for mean lives greater than, say a few days, can be obtained from
the underground experiments of Reines et al. [3] on the degree of accuracy
with which the baryon conservation law is known. In these experiments it
was found that the carbon nucleus has a mean life longer than 10 27 y (for
high energy decays). If we take into account that the carbon compound,
of which the detector was made, had been irradiated at the earth surface
by a cosmic ray nucleon flux of 10~ 4 to 10 5 cm 2 s 1 , the upper limit for
the production crosssection by nucleons of a radioactive quasinucleus turns
out to be quite large — 10 30 cm 2 /nucleus.
214 B. Pontecorvo
3*1. Possibilities of the method proposed.  Let us discuss now what pos
sibilities are given by the method just proposed. An estimate will be made
for the case of the Serpukhov accelerator, although it is clear that such
experiments could be performed on an accelerator of the CERN, Brookhaven,
or SLAC types. Let us consider for example a mean life of the new type
of radioactivity of the order of days ; in such a case the radioactivity can be
investigated far away from the accelerator, in conditions of low cosmic ray
background. In spite of the fact that radiochemical separations will not be
considered here, still a detection efficiency of about 0.2 or more can be achieved.
With an average intensity of 10 12 protons/s, at saturation it is possible to
detect the production of radioactive quasinuclei with a crosssection of the or
der of 10~ 40 cm 2 /nucleus, which corresponds to about one decay event per day.
If the production crosssection of quasinuclei by protons colliding with nuclei
is known, one may then obtain the crosssection for the production of new par
ticles in nucleonnucleon collisions after the introduction of a small coefficient.
It is just the requirement that the new particle is found inside the spallation
product which leads to the necessity of introducting this small coefficient, the
value of which, of course, cannot be estimated a priori. However, if we fantas
ticate on the analogy between the process considered ihere and the wellknown
process of hypernucleus production, we may give a rough estimate, starting
from the corresponding experimental data on hypernuclei. It is known that the
probabilities of hypernucleus production in photoplates by K mesons of energy
3, 5 and 10 GeV are (3±0.1)% [4], (2.2±0.1)% and (1.2±0.1)% [5] of the
total nuclear collision probability, respectively. Unfortunately at present there
are no available data for higher energy kaons, but from the quoted informa
tion, and also from the fact [6] that for 25 GeV protons the fraction of nuclear
interactions in emulsions which results in hypernucleus formation is 0.5%,
we may guess a value of 0.005 for the indicated small coefficient.
Thus the proposed method is capable of revealing crosssections for the
formation of new particles in nucleonnucleon collisions which are ten orders
of magnitude smaller than the total nucleonnucleon crosssection (of course,
if the assumptions made are true).
3'2. Remarks on the proposed method.  If possible, the irradiation of the
target should require a time comparable with the mean life of the activity
which is looked for. For short mean lives one should use the extracted par
ticle beam (at Serpukhov such a beam will consist of 30 proton pulses the length
of each pulse lasting 1.5xl0~ 8 s); this permits us also to take the measure
ments in the immediate proximity of the target. By means of the classical
delayed coincidence method (when the radioactivity is looked for in the time
interval between accelerated proton pulses) one may search for mean lives of
Search for new stable particles 215
the order of 10 8 s with effective beam intensities of a few percent of the
full beam intensity and of the order of 10~ 6 s or more at full beam intensity.
When investigating mean lives from 10~ 8 s to a few microseconds one must
pay attention to the pion and muon background.
By the way, when searching for the new type of radioactivity with a mean
life in the microsecond region, the most adequate beam time structure is to
be found in electron linear accelerators (SLAC and Kharkow), where the beam
time length is of the order of microseconds with a repetition rate of 100 Hz.
An extracted proton beam is convenient also when looking for mean
lives less than a few hours, although in such a case the internal target may
be used.
The shortest mean life which can be looked for in the internal target of
the Serpukhov accelerator is of the order of milliseconds (as such is the time
required to put the target into the beam). If the internal target is used, it is
highly desirable to take measurements in one of the straight sections, because
this allows a larger solid angle to be seen by the detector at the target.
In the search for activities with mean lives greater than a few hours, the
internal target can be removed and investigated in conditions of very low
cosmic ray background and a high solid angle detector. One can consider
the possibility of using a liquid internal target, which can be easily removed
from the vacuum chamber.
In the search for « radioactivities » with long mean lives there are two
difficulties which are present also, to a less degree, in the search for shorter
mean lives.
1) The main source of background is due to cosmic ray muons, the
integrated flux of which at the earth surface is about 0.01 cm 2 s _1 , and
also to nuclear « stars » produced by cosmic ray neutrons. It is evident that
investigating the target « radioactivity » underground has great advantages
in the search for long mean lives. In the most deep existing underground
laboratories the cosmic muon intensity decreases by a factor of 10 8 . In such
conditions there is no background even in the absence of an anticoincidence
system. Such system, which can easily decrease the muon background by
a factor of 1000, should be used if the measurements are made near the earth
surface.
2) The irradiated target is strongly active due to the presence of spalla
tion products. This has the effect that no full advantage for decreasing the
cosmic ray muon background can be made of the fact that a target of very
small dimensions (say < 1 cm 2 ) can be used ; as a matter of fact, there will
be many accidental coincidences between the counters through which pass
cosmic muons and the small area counter, placed in the immediate proximity
216 B. Pontecorvo
of the small target. It may be necessary to place a filter between the target
and the detector to decrease strongly the beta radioactivity.
One of the detector elements must be an energy spectrometer, let us say
a Nal chrystal (or a lead glass spectrometer, etc. if high energy gamma's
are looked for).
If the measurements are made at the earth surface it may turn out to be
necessary to use some kind of track chamber to reject the events in which
the particles are not coming out of the (small) target.
Here I would like to mention another possible registration arrangement.
When a heavy (Z>80) quasinucleus decays, the decay products may in
duce with reasonable probability the fission of the nucleus. Consequently
there raises the probability of searching for a « radioactivity » with emission
of fission fragments in a thin heavy target (made of an element not under
going spontaneous fission, let us say Th) irradiated by highenergy particles.
The interest in this arrangement is due to the possibility of detecting (even
at the earth surface) very rare fission events of a substance having an ex
tremely high beta activity.
One might also consider the search, deep underground, for a delayed emis
sion of a few neutrons from a heavy material irradiated by highenergy par
ticles, because it is well known that a heavy nucleus excited at a few hundred
million electronvolts emits many evaporation neutrons.
4.  Conclusion.
The wellknown methods of observing neutral particles (decay in fight,
missing mass spectrometer) are adequate only if the mean life is short enough
or if the corresponding production crosssection is relatively large.
It is evident that the present proposal (a search for a « radioactivity » of
a special type) is quite naive, a fact which I fully recognize. However the
proposal is relatively simple and, independent of the ideas expressed in this
paper, the suggested experiment has a definite phenomenological interest.
It is a pleasure for me to thank R. Vassilkov, L. Landsberg, L. Okun,
M. Markov, L. Nemionov, A. Ciudakov for support and discussions.
Note added in proof.  After this paper was written, Dr. Giacomelli has kindly informed
me about an interesting investigation [7], which is relevant to the question discussed above
from an experimental point of view, although it originated from a completely different
« phylosophy ». A search was made for magnetic monopoles, which might have been
Search for new stable particles 217
produced in collisions of highenergy protons with nuclei. In order to detect the products
of a possible monopoleantimonopole annihilation, the authors lookedfor a high energy
radiation from a target irradiated by 27.5 GeV protons. No effect was found, the detector
being sensible to electrons and photons in the time interval from 0.1 s to 1 day after
the « production of the monopoleantimonopole pair » in targets of Al, polyethilene, and Cu.
According to this investigation the upper limit for the production crosssection in light
elements of a radioactive quasinucleus of the type discussed in this paper turns out to
be several orders of magnitude smaller than that from ref. [3].
REFERENCES
[1] See for example, Antipov et al.: Phys. Lett., 29 B, 245 (1969).
[2] See for example, L. Okun: JETP, 47, 1777 (1964).
[3] H. Gurr, W. Rropp, F. Reines and B. Meyer: Phys. Rev., 158, 1321 (1967).
[4] J. Lemonne et al.: Nuovo Cimento, 41, 235 (1966).
[5] G. Coremans et al.: Nuovo Cimento, 61, 525 (1969).
[6] J. Zakrzewski: Proc. Intern. Conf. Hyper fragments (Geneva, 1964).
[7] M. Fidecaro, G. Finocchiaro and G. Giacomelli: Nuovo Cimento, 22, 657 (1961);
E. Amaldi: On the Dirac Magnetic Poles, Old and New Problems in Elementary Par
ticles, edited by G. Puppi (Academic Press, New York, 1968).
The Isobaric Analog Resonances
in Phenomenological Nuclear Spectroscopy.
R. A. Ricci
Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Legnaro  Padova
Istituto di Fisica G. Galilei, Universitd di Padova  Padova
1.  Introduction.
The remarkable achievements of nuclear spectroscopy in the last ten
years have been made possible by the advent of new types of high resolution
accelerators, such as Tandem Van de Graaff, to produce particle beams in
a large interval of masses and energies, and by the solid state detectors upon
which the socalled « in beam nuclear spectroscopy » is based. These tech
nical advances have allowed measurements that only a few years ago were
impossible and a considerable volume of new information is now available
for theoretical investigations. A large number of nuclear states have been
identified and classified by means of precise determinations of energy, an
gular momentum, parity, and transition probability. A systematic knowledge
of such attributes of nuclear levels is essential for any attempt to relate them
theoretically and provide the experimental ground for testing the validity
of the current microscopic theories the goal of which is to disclose the fun
damental features of the nuclear structure.
The aim of this paper is to give a comprehensive outline of the socalled
isobaric analog resonances, a promising and relatively new topic in nuclear
physics. The outstanding importance of the isobaric analog resonances
(IAR) is brought about by the fact that in many cases they give the clue for
the correct interpretation of the observed structures in nuclear excitation
spectra.
It is well known that the low excitation levels (bound states) are charac
teristic of the collective motion of the nucleus, namely rotation and/or vi
bration modes or motion of mutually interacting particles. This situation
corresponds to an average width r (decay probability) very small as com
Isobaric analog resonances 219
pared to the average distance D between levels, i.e., J 1 <C D. By gradually
increasing the excitation energy, the level density also increases and, above
the nucleon threshold, the nucleus « enters » the continuum region. In the
neighborhood of this region the nuclear states, obtained through capture
reactions (formation of the compound nucleus), decay to the levels of the
residual nucleus and the yield relative to the different exit channels exhibits
a resonant behavior (compound nucleus resonance) : Since r is of the order
of D (r~D) the resonances are observed separated provided the measure
ments are carried out with adequate energy resolution (§£'</').
At higher excitation energies the situation becomes more complicated
due to the overlap of the nuclear levels. The existence of statistical fluctua
tions, namely a sort of background noise due to the behavior of the reac
tion amplitudes, is nowadays a wellestablished fact. The reaction partial
amplitudes, randomly distributed over a large number of levels, sum up
coherently with a width r c (coherence width): this implies that when 8E<T,
namely when the measurements are performed with high resolution, the fluc
tuations can be observed as superimposed to an average behavior generally
nonresonantlike [1]. Characteristic resonances, however, can distort the
nonresonant behavior: evidence has been obtained in the last few years of
such an anomalous behaviour in experiments with not very high energy res
olution. This kind of resonances has been called « intermediate structures »:
They correspond to peculiar nuclear states, completely determined by the
entrance channel, which give rise to the excitation of resonances of the com
pound nucleus through particular correlations (doorway states) [2]. The im
provement of the resolution brings to view a fine structure composed by
several narrow resonances which should be properly correlated in order to
give the single gross resonance observed in experiments which de facto aver
age the reaction crosssection. It is evident that a clearcut identification of
an intermediate structure is bound to the fact that the observed effect on
the crosssection be unambiguously independent of any averaging procedure.
It is conceivable that by virtue of some specific interaction the doorway
state mixes coherently in the resonant region with the compound nucleus
resonances nearby localized. The stronger such a mixing is, the more cor
related are the nuclear states with the entrance channel, contributing to the
intermediate resonance and more crucial is the effect of the presumptive
doorway state on the decay behavior of the compound nucleus. So far these
predictions have not yet been corroborated by a clearcut experimental sup
port because of the difficulty of performing measurements satisfying the fol
lowing conditions [3]:
D z >r It D z ^D,2r,
220 R. A. Ricci
where Z> 7 is the average spacing of intermediate states and .T z is their average
width, while D and r refer to the compound nucleus. There are two cases
where the above conditions are fulfilled : the giant resonance and the isobaric
analog resonance.
2.  Isobaric analog states as resonances.
The essential standpoint was the discovery of the possibility of producing
isobaric analog states as compoundnucleus resonances in reactions initiated
by lowenergy protons (below the Coulomb barrier) on medium and heavy
nuclei. The pioneer experiment was performed by the Florida State group [4]
who found strong anomalies in the excitation curve of the 89 Y(p, n) reaction
clearly arising from the 89 Y+p compound system ( 90 Zr) and reproducing with
good accuracy the intervals of the lowlying bound states of the 89 Y+n ( 90 Y)
isobar.
The standard analysis of the elastic protonscattering data revealed the
exact correspondence of spin and parities ; moreover the « analog spectrum »
was found to be displaced relatively to the isobaric « parent spectrum » by
the expected Coulomb energy difference. This was the second important
step in the modern history of the isobaricspin nuclear spectroscopy. The
first one was the identification of new modes of excitation in chargeexchange
reactions as isobaric analog states. The anomalous sharp peak found in the
neutron evaporation spectrum following the 51 V(p, n) 51 Cr reaction by Ander
son and Wong [5] was interpreted as the isobaric analog of the target ground
state. Since then this situation was found to hold for other heavier nuclei
and not to be restricted to light nuclei as it was believed for a long time.
These experiments and their interpretation in terms of isospin dependence
of the optical potential, as given by Lane [6], opened the current interest
in isobaric analog states (IAS) and buried the old superstition that the clas
sification of nuclear states in terms of isobaric spin was useless for medium
and heavy nuclei (i.e., Z> 10) because of the strong Coulomb interaction.
In this connection it is worthwhile to mention that since 1961 French and
Mac Farlane [7] have introduced the concept of isobaric splitting in describing
the distribution of spectroscopic strengths in particletransfer reactions even
in mediumweight nuclei.
In fact, the use of isobaric spin in nuclear spectroscopy since the theory
developed by Wigner in 1937 [8], was strictly connected with the occurrence
of isobaricspin multiplets in the assumed chargeindependent nuclear world.
In this world the knowledge of the properties of one member of a given
multiplet is sufficient to describe completely the other members (the « isobaric
Isobaric analog resonances 221
analogs » of the former). However, the nuclear Hamiltonian is not exactly
chargeindependent; in the limits that chargedependent effects such as the
Coulomb interaction between protons are not so strong to cancel the regu
larities predicted by the chargeindependent part, the isobaric spin is still a
good quantum number. In light nuclei the Coulomb mixing is only a very
slight perturbation because of the quite large average spacing between states
of different isospin ; consequently, isobaric multiplets were found to hold in
this case with analog states obtained by simply applying the chargeexchange
operator T~ to the parent states.
The situation is different for medium and heavy nuclei, where the sym
metry and pairing energies can put the analog states in the continuum region
and the strong Coulomb interaction can mix them with nearby states of
different isospin ; moreover they can become proton unstable, while the parent
states (lowlying) are stable against particle emission (bound). The con
nection between such states cannot be simply assured by the T~ operator and
the isobaricspin correspondence may be completely destroyed.
The discovery of isobaric analog resonances (IAR) has been taken as an
indication of the survival of the isobaricspin (chargeindependent) description
in the continuum region, where the IAS can be interpreted as some kind
of « special states » embedded in a dense spectrum of complicated com
poundnucleus states [9].
A schematic picture of the correspondence between such IAS and parent
states is shown in Fig. 1.
The (Z — 1, N+l) and (Z, N) nuclei are connected through the charge
exchange operation (n^p); neglecting the Coulomb interaction, it may
happen that the levels of the former ones are located at exactly the same
energy in the continuum region of the latter ones. Due to symmetry effects
in the nuclear interaction, the displacement of the states r> and T< is ex
pressed by the term £ sym the value of which for medium and heavy nuclei
may be higher than the threshold for neutron emission. Without Coulomb
interaction the states T> in the (Z, N) nuclei would have exactly the same
configuration of the parent states in the (Z— 1, jV+1) nuclei; because of
the isospin difference, these states do not mix with those of the continuum
and therefore are bound states.
The Coulomb interaction gives rise to a displacement of the spectrum of
the (Z, N) nucleus which amounts to the difference A£c (*) between the
Coulomb energy of the two systems; furthermore, the proton emission
(*) The term AE C considered here accounts also for the neutronproton mass dif
ference which should be included in the atomic mass scale. Only relative shifts are
considered here.
222 R. A. Ricci
with Coulomb without
interaction Coulomb int.
analogue states
Z^N
T=T.=
NZ
Fig. 1.  Correspondence between isobaric analog and parent states with and
without Coulomb interaction in a typical medium or heavy nucleus.
threshold is lowered and it may occur that the analog states become unstable
against proton emission. In this case it is possible to excite an analog state
as a resonance by means of elastic scattering of protons. It has to be re
marked that the Coulomb interaction favors the mixing of the T> state with
jhe neighboring ones correlated with it by the same set of spin and parity
Isobaric analog resonances
223
attributes. In this way, exit channels responsible for the decay of the T<
states are open; it follows that, by virtue of chargedependent effects brought
about by the Coulomb mixing, an analog state becomes indeed observable
through an isospinforbidden decay (for example, neutron emission). In the
first experiment carried out by the research group of the Florida State Uni
versity [4], which led to the discovery of the isobaric analog resonances,
anomalous nuclear structures were observed in the excitation curve of a
(p, n) reaction.
In conclusion, an analog state in the continuum appears as an inter
mediate structure induced by an elementary excitation, namely a charge
exchange interaction, which stimulates the excitation of the neighboring
states of the compound nucleus through the Coulomb mixing and acquires
their decay properties.
3.  Production and decay modes of IAR.
Figure 2 shows a schematic diagram of a protoninduced reaction with
excitation of IAR and the isospinallowed and forbidden decay of these latter.
,t E P
(Z1.N)
target nucleus
nuclei
(Z,N)
T 2 NzZ
(Z1,N+1)
parent nucleus
■z 2
Compound nuctous
Fig. 2.  Schematic diagram of a protoninduced reaction with production of
IAR; the neutron or adecay of IAS is made possible by the coupling with
the normal T < compound nucleus states.
224 R. A. Ricci
The bombarding proton energy (in the centerofmass) needed for ex
citing IAS via a resonance reaction is:
£c.m. = A£ c — Sn ,
where A£c is the Coulomb shift and S a the neutron separation energy.
In light nuclei, in spite of the low Coulomb barrier, states which are the
analog of lowlying bound states cannot be excited in resonance reactions,
since &E C < S a . Now, AEc increases with Z while S n decreases slowly with
increasing A; consequently IAR become available for medium and heavy
nuclei. On the other hand the required proton bombarding energy becomes
higher and higher; this explains the fact that such experiments are generally
done with Tandem accelerators which cover the energy interval required
for a large amount of nuclei and whose energy resolution is far superior
to the energy resolution of either the incident proton or the outgoing par
ticle detection devices.
Nevertheless, in recent years, some interesting investigations on IAR
have been performed even at subtandem energies (up to 5.5 MeV) with Van
der Graaff accelerators in connection with properly used proton and gamma
highresolution spectrometry. In fact, the available experimental data on the
finestructure and gammadecay properties of IAR have been obtained mostly
at subtandem energies and in the region of medium weight nuclei (2sld
and 1/j shell).
These properties are of fundamental importance in the analysis of IAR
and the related spectroscopic information. Furthermore, the standard elastic
scattering analysis in terms of interference pattern between resonance and
potential scattering allows the extraction of spectroscopic parameters (reduced
proton widths) related to the properties of the parent bound states.
3'1. Elastic scattering and spectroscopic information.  An IAS in the
continuum is a resonance. A fundamental problem is to explain how it can
be putted in the same isobaric multiplet of a bound state. More precisely,
the fundamental task is to understand the connection existing between the
appearance of an isobaric analog resonance and the strict isobaric corre
spondence with a bound state and what role is played by correlations, dif
ferent from the simple Coulomb mixing, between the entrance channel and
the normal compound nucleus state in generating the observed resonance.
Several theoretical approaches attempt to find an answer for all these open
problems and to develop reliable methods for the analysis of excitation curves
with the final goal of extracting the spectroscopic parameters characterizing
the IAR [9, 10,11].
Isobaric analog resonances
225
From a phenomenological point of view, which is of interest here, the
IAR observed in proton elastic scattering can be related directly with the
corresponding parent states via their spectroscopic properties. A typical
curve for a (p, p) elastic excitation function is shown in Fig. 3.
The curve is analyzed in terms of a resonance plus potential scattering
yielding to the resonance energy E R , the total width r, and the partial pro
ton width r p ; moreover, the interference pattern observed at different scat
"Zrlp.pJ^Zr
0)
<**
'c
f ^K 165°
\J Ep crn ( MeV )
i i i
300 
200 
100
5.8
6.0
mb
6.2
92 Zr(p,n) 92 Nb
cm
Ep" m (MeV)
5.7
5.8
5.9
6.0
6.1
6.2
63
Fig. 3.  The excitation function for elastic proton scattering on 92 Zr in the
region of the 93 Nb groundstate isobaric analog (schematic, see ref. [12]). Also
shown is the neutron excitation curve for the 92 Zr(p, n) reaction in the same
energy range.
15
226 R. A. Ricci
tering angles yields to the proton angular momentum / p and consequently
to the parity, and, in some cases, to the spin of IAR. The spin is uniquely
determined when also the polarization of the scattered protons could be
measured [13]. The correspondence with the isobaric parent state is first
given by energy and quantum numbers. Furthermore, a clear correlation
exists between the elastic width and the stripping spectroscopic factors of
these states.
From Fig. 2 it is seen that the low excitation states of the parent isobar
(T '—T z = T>) may be produced by means of a stripping reaction through the
transfer of one neutron to the same target nucleus. The spectroscopic infor
mation thus obtained concerns not only the energy, spin, and parity but also
the spectroscopic factor Sd.p, which, in singleparticle reduced width y >p
units, expresses the reduced width y\ for neutron capture into a bound parent
state: S d>p = yljy% .
Starting from the same target state the elastic scattering crosssection for
the analoge resonance yields to the reduced width y\ for proton capture
into the analog state, through the relation y% =r^ bs /2P l , where r° bs is the
observed partial width and P z is the trasmission coefficient which allows the
proton to traverse the momentum discontinuity at nuclear surface and to
penetrate the angular momentum and Coulomb barrier.
If T is the isobaric spin of the target the isobaric analog state spends only a
1/(2T" +1) fraction of the time as a proton state; consequently:
yl i
yl 2T +i'
i.e.,
y* p 2r +r d ' p 
This result gives the correspondence between the nuclear structure of the
analog resonance and that of the parent state through the correlation with
the same initial state (target nucleus). Unfortunately, current methods used
for extracting the spectroscopic factors by means of distorted wave analysis
give results affected by large uncertainties (of the order of (20^30)%),
whereas the determination of the reduced width from elastic scattering ex
periments is generally limited because of difficulties in evaluating correctly
the trasmission coefficient which may be modified in a complicated way by
the presence of the !T< states. The study of the IAR will become an independent
spectroscopic tool of outstanding importance as soon as appropriate methods
will be developed for the determination of accurate spectroscopic factor
from the data [9]. So far the study of the inelastic scattering through the
Isobaric analog resonances 227
IAR seems to be more promising. In this case, the excited states of the target
nucleus are correlated with the isobaric analog resonance. The comparison
of the inelastic and elastic excitation curves gives information on the config
urations existing in those states.
3*2. Fine structure.  The « gross anomalies » observed in proton elastic
scattering have generally total widths of the order of 10 times the widths
expected for the normal compoundnucleus resonances. This is what is found
in poorresolution experiments and is generally interpreted in terms of a
« gross structure » averaging over individual resonances just as an inter
mediate state. The main effect of the 7"> resonance is associated with the
interference between Coulomb and resonance scattering. However, the shape
of the gross anomaly shows some departures from the pure BreitWigner
form, with a typical asymmetric behavior (see Fig. 3).
This was interpreted by Robson [9] in the framework of the i?matrix
theory as a consequence of a coherent interference between two contribu
tions arising from two different regions of the configuration space: one is
internal to the nucleoncharge distribution (r < re), where T< is a good
quantum number (no Coulomb mixing); the other is the external region
allowing Coulomb mixing. When the two solutions of the Schrodinger equa
tion are smoothly joined in order to calculate the collision matrix, the presence
of the T> IAS contributes to the widths of the normal compoundnucleus
states with the same attributes defined in the internal region, giving rise to
an enhancement of such states. This enhancement is asymmetric as a function
of the energy and vanishes just at the energy of the IAS, which is found to be
higher than the energy at which the elastic resonance occurs.
This prediction was confirmed in the highresolution experiments where
the fine structure of IAR resolved. The typical example is shown in Fig. 4,
where the fine structure covered by the IAR found in the 92 Mo(p, p) exper
iment is seen to quench more rapidly on the highenergy side of the excita
tion curve.
We are dealing, in this case, with a typical heavy compound nucleus ( 93 Tc)
with high normal level density in the analog state region; then the fine struc
ture is interpreted as being due to the fluctuations of many overlapping levels
with the same spin and parity as the analog one (r>) but with lower isospin (T<).
This is related to the fact that the best fit to the experimental crosssection,
in the poor resolution measurement, yields a partial proton width r p which
accounts for only ~ \ of the total width r B ; r p = r R would have been ex
pected in this case, since we are below the Coulomb barrier and the sole
proton channel is open [15]. More insight in this matter is gained when the
experiment can resolve all the T< individual components in the region of the
228 R. A. Ricci
E x (MeV)
dc/dXl
1 300
Q(p.n)
r rir
 Ep cm « 5.24 MeV
250
Mo + n
 92 Mo + p \
 ae c «i;
: 1
2.28 MeV 25
U9
20
93 V2+
A2 Mo 51
T=9/2
93 Tc V
T< = 7/2
92'
90°
_i i i i_
T 0.25 keV
Ep(MeV)
528
5.30
532
Fig. 4.  Gross and fine structure of the IAR corresponding to the 93 Mo ground
state (T=T Z = %) in the 92 Mo(p, p) reaction (schematic, see ref. [15]). On
the lefthand side the schematic diagram of the reaction is shown.
analog state. Few experiments of this type have been performed so far, all
confined to mediumweight nuclei such as 41 K [16], 49 Sc [1720], 23 Na [21],
43  45 Sc [22]. It is interesting to note that, due to the rather low neutron sep
aration energy in all these cases such experiments have been performed at
subtandem energies (i.e., with the Van de Graaff accelerators of the Duke,
Padua and Utrecht Universities). The high overall resolution obtained in
these experiments (from 0.2 to 0.8 keV) could separate the individual com
poundnucleus resonances averaged over by the IAR. In fact we are dealing
here with nuclei where the level density at the IAS energy is not so high as
in heavier nuclei, so that the best energy resolution actually available from
accelerating machines is enough for such measurements.
All these experiments clearly show that the sum of the partial widths r pX
is less than the total width r R of the intermediate resonance, i.e., the tails of
the individual resonances add coherently to produce one large resonance
with a great amount of nonresonant range inbetween. The difference
W=T R — ^r pX is the socalled « spreading width » (statistical contribution
in the region of the IAS).
Figures 5 and 6 show schematically two typical examples of fine structure
experiments, the first one being the 40 A+p reaction with essentially the proton
Isobaric analog resonances
229
channel open [16], the second being the 48 Ca+p experiment where also the
neutron and gammaray channels are open and indeed measured [1719].
In the first case 17 individual resonances were found, every one with spin
and parity f _ and with a distribution corresponding exactly to the shape
of the LaneWignerThomas giant resonance in 41 K; this « microgiant »
resonant structure corresponding to the analog strength being shared among
the surrounding normal states, was already predicted by Bloch and Schiffer [23],
for the case where the spacing between such states is much less than the mixing
strength. The enhancement of the compoundnucleus resonance appears clearly
as due to the mixing with the nearby analog state, while the fact that, for
each resonance, r p <T shows the presence of a nonvanishing spreading
(damping) width, arising from the coupling with other nonresonant degrees
of freedom of the target plus proton system [11].
In the second case the IAR corresponding to the 49 Ca groundstate isobaric
analog in the 48 Ca+p ( 49 Sc) system was resolved in individual components
singled out in the isospinforbidden (p, ny) reaction [17] performed with
the 5.5 MeV Van de Graaff of Padua indicating a more detailed structure
than that found in a first (p, p) experiment with not very high energy resolu
tion [19]; a successive highresolution elastic scattering experiment performed
at the Utrecht Van de Graaff accelerator [18] confirmed the presence of at
10
r 5
Uj
E  1.825 MeV
p
/_
A + p
a)
T =5/2
r = 800 eV r= 1250 eV
j — i — i i i i i_
.86 1.87
E (MeV)
 T
3/2
Fig. 5.  Reaction diagram (a) and fine structure (c) of the 1.87 MeV IAR found
in 40 A(p, p) experiment at Duke University [16] (schematic); the IAS (7^ = f)
corresponds to the fourth excited state (T = f , / = f") of the parent 41 A. The
corresponding gross structure found earlier at Yowa [12] is also shown sche
matically (b).
230
R. A. Ricci
Ex(MeV)
10 
T>= 9/2
48
Ca+p
J
Ep c =1.935 Me'
LQJB.QJT. ^Sc
AE r = 7.081 MeV
&■
49 Ca
T=9/2
46
Ca+n
49
i/i
Sc
21 3t 28
T<=7/2
8x10 3 A ^rp1.5keV
3/2 172 «
6
1.95 1.96 1.97 1.98 1.99 200
«labu
Ep iaQ (MeV
Fig. 6.  Reaction diagram for the excitation and decay of the 49 Ca ground
state IAR in the 48 Ca+p system, and corresponding fine structure found in
(p, p) and (p, ny) experiments (refs. [17] and [18]).
least 7individual resonances with the expected f assignment and with 2^p* =
= (2.2±0.3) keV rather smaller than the singleparticle value 4.4 keV obtained
from the stripping spectroscopic factor Sd, P = 1 found in the 48 Ca(d, p) 49 Ca
reaction [24]. A similar result has been obtained in the recent experiment
performed at Duke [20], where an additional §~ resonance has been found
and a value of 1.85 keV for the sum of the proton widths has been reported;
this value, compared with the estimated [19] width for a singleparticle (f  )
resonance, gives a spectroscopic factor .Sd.p = 0.6.
3'3. Shell model description of IAR.  The 48 Ca+p system is interesting
from several points of view. First, it corresponds to a particle outside a doubly
closed shell core ( 48 Ca has Z = 20 and N = 28) ; consequently it is a case
suitable for a shellmodel description of the isobaric analog resonances [10, 25].
Isobaric analog resonances
231
The basis for a microscopic shell model analysis of IAR is the particlehole
picture of Bloch and Feshbach [2], where the nucleonnucleon interaction
allows the mixing between the virtual state of the proton plus target system
with a 2 particle 1 hole state in the compound nucleus; such 2p\h state is
the doorway state with isobaric analog configuration (T = T>), giving rise
to the intermediate structure in the presence of the neighboring T< states;
these latter correspond to much more complicated configurations (3p2h, etc.).
The particlehole picture for the 49 Ca groundstate analog is schematically
represented in Fig. 7.
•hell p ! n
48.
W ( Ca )
ANALOGUE T,  T + 1/2  9/2
2s1d
np
•
1
I
s,
<M
W,
p
§
PARENT
49 Ca
T z To+V*9/2
Z N
1 p state
2 T ( 2 p  1 h ) states
COMPOUND : 48 Ca+p
TrToV27/2
Fig. 7.  Particlehole picture of the 49 Ca groundstate analog configuration.
The 2p\h configuration corresponds to one neutron in the 2/? shell and one
proton and one neutronhole in the lf^ shell; since there are 8 neutrons in the
1/? shell, there are 2T modes of obtaining the 2 particle  1 hole doorway state
(T Q = 4 is the target isospin).
The 2plh state serves as an intermediary between the incident proton
and the complicated 3plh states, since it can mix with them while the proton
entrance channel cannot; the doorway can decay into the T< states forming
an intermediate structure, whose total width is given by
r R = r\+r\,
where r^ is the « escape width » for the singleparticle decay in the con
tinuum and ri is the « damping width » (corresponding to the spreading
width already mentioned) i.e., the decay width into more complicated modes.
Now r"t = ^ r t , where the index / refers to all the open exit channels (i.e., p, n
232 R. A. Ricci
and y in our case), consequently
Following the results of refs. [1719] and the analysis of the intermediate
structure performed in ref. [19], one has
r p + T„ = (2.4 ± 0.5) keV (refs. [17, 18]) = (3.4 ± 0.8) keV (ref. [19]) ,
T Y =0.24eV (ref. [18]),
r R = (4.7 ± 0.4) keV (ref. [19]) ,
r exp =(2.3 ±0.7) or (1.3±0.8)keV,
theory = 0.6 keV (ref. [19]).
A better evaluation of the widths for the isospinforbidden neutron decay
seems to be necessary in order to ascertain if there is a real discrepancy
between the experimental and calculated damping width; this is of some
importance since a large spreading width corresponds to the interference of
other possible degrees of freedom to be considered in a suitable classifica
tion [11].
3"4. Neutron decay.  A second interesting aspect of the 48 Ca+p exper
iment is the presence of the neutron exit channel. Since it is generally assumed
that the lowlying levels of the residual nucleus arising from the (p, n) reac
tion ( 48 Sc in the present case) are normal T< = T z = T — 1 states, with
reasonably pure isobaric spin, the neutron decay from the r> = T + ^
IAS should be forbidden (Ar = f ) (see Figs. 2 and 6). As already men
tioned, its occurrence is taken as an indication of the mixing between the IAS
and the surrounding T< states ; on the other hand this makes it possible to
characterise the IAR through the sharing of its strength among the normal
compoundnucleus states. The case in point here is a typical example.
Indeed it was found in a first poor resolution experiment (see ref. [17])
that the neutron decay at a proton bombarding energy corresponding to the
gross resonance was selective for the residual states of 48 Sc. In other words,
there exists a preferential decay of the analog state to one of the levels of the
residual nucleus (due to a particular configuration of the latter one), namely
to the level at 1 .4 MeV which undergoes a strong gamma transition of
0.78 MeV. The yield of this transition, determined by means of gamma
spectroscopy, provides an excellent measurement of the excitation of the
analog resonance and of its fine structure. This is clearly seen in Fig. 8,
where the yields of 0.78 MeV and 0.37 MeV Yrays are compared, the latter
Isobaric analog resonances 233
48
Ca(p.nj) Ej= 0.78 MeV
JU
Ej= 0.37 MeV
2.K) 2]2
Ep ( MeV )
Fig. 8.  Yields of the 0.78 and 0.37 MeV yrays following the neutron decay
of the 49 Sc compoundnucleus in the region of the T = § , / = f IAR, in the
48 Ca(p, ny) experiment, a) E y
0.78 MeV; b) E y = 0.37 MeV.
one being originated in transitions from a lower level which collects most of
the neutron decay from the compound nucleus states. The selection of the
0.78 MeV yray allows, therefore, the suppression of the background due to
resonances and decay modes different from those mixed with the analog
state.
Another interesting fact is that the shape of the enveloping distribution
is almost Gaussian, as is expected in as much as the entrance channel can
only produce the higher isospin and the neutron emission can only proceed
from the lower isospin; the asymmetry of such a distribution is less pronounced
than in other typical cases, where a dip is found in the neutron excitation
curve just at the energy of the IAS at which the isospinviolating processes
should vanish following the LaneRobson model (see Fig. 3).
3'5. Gamma (radiative)decay.  The third point of interest in the present
example is the determination of the gammadecay properties of the IAR.
Such properties are of considerable interest in nuclear spectroscopy, since the
gammatransition probabilities are strongly correlated with the intrinsic struc
ture of the nuclear states. In fact it has been pointed out that the gamma
decay of IAS observed in (p, y) reactions may be very simple [26]. Let us
consider the case of quite pure IAS (r> = 7^+1) with singleparticle
character in the compound nucleus formed in a (p, y) reaction ; in the same
234
R. A. Ricci
T>= 9/2 = Tp + 1/2
Compound nucleus
T>=T +1/2
J = 3/2
Sd . p f f rom A8 Sc ) 0.6 \ t T<=7/2 = T  V2
* J« 3/2
W/2
J7/2
""Sc
21 28
Fig. 9.  Schematic picture of isospin splitting of a singleparticle state as a
result of its coupling with a J = core. The 48 Ca+p case is illustrated with
the result found in (p, y) reaction (ref. [18]).
nucleus at least 1 bound state with exactly the same nuclear configuration,
but with different isospin symmetry (T< = T z ) exists, due to the isospin
splitting of singleparticle states [7] (see Fig. 9). Such a state is called an
« antianalog » [26] or « homolog » [27] state and should be connected with
the IAS via a strong Ml transition [28] of the order of the Weisskopf unit.
The work of the Utrecht [26] and Ohio [28] groups in the 2sld shell was
successful in locating, through (p, y) reactions, several strong IAR with rather
little isospin mixing and strong Ml analog to antianalog transitions. Such
cases are rather simple, because only the channels for proton and gammaray
emission are open, the analog and antianalog states are essentially not frag
mented and the corresponding gammatransition connecting them stands out
clearly in the gammaspectrum taken at the resonance energy.
This is due to the weak coupling between the singleparticle state and the
core which forms a (7 , <, 7^) doublet with spin J = j if the core is a J =
nucleus (see Fig. 9). Theoretical calculations performed by Maripuu [29]
show that a strong enhancement of Ml transition rates between the two
members of the isospindoublet arises for the « parallel » case J = j = / + 
(i.e., when the orbit and the spin of the added proton are parallel) as com
pared with the « antiparallel » case J=l—%. The experimental data in the
Isobar ic analog resonances 235
2s\d shell nuclei generally agree with these predictions. A rather different
situation is found in the 1/j shell, where data concerning 49 Sc (we are discussing
here), 49 V [30] and 51 V [31] are now available.
In the 49 Sc case, for instance, the coupling between the \p§ singleparticle
state and the 48 Ca core seems not to be weak so that it becomes fragmented,
especially for the lower (r<) member; moreover, as we have seen, the IAS
is rather strongly mixed with the neighboring compoundnucleus states with
complicated configurations. The gammabranching from the IAR is then
less simple, but could give important information for a microscopic description.
The result found in the 48 Ca(p, y) experiment [18] show the presence of
an E2 groundstate transition from the major resonance present in the fine
structure of the IAR and the absence of Ml transition (less than 6 x 10~ 4
Weisskopf unities) to the expscted strongest fragment of the antianalog
state (the 3.08 MeV level with stripping spectroscopic factor of about 0.6).
This could be related to a much more fragmentation of the 1/7$ singleparticle
state and to a strong mixing of the IAS with more complicated (3plh) con
figuration at such a resonance energy.
I would like to express my gratitude to my friend Professor C. Villi for
critical reading of the manuscript.
REFERENCES
[1] See for instance, T. Ericson and T. MayerKuckuk : Ann. Rev. Nucl. Sci., 16 (1966).
[2] See for instance, B. Bloch and H. Feshbach: Ann. Phys., 23, 47 (1963).
[3] Cfr. C. Bloch: Intern. Conf. Progress Nucl. Phys. with Tandems, Heidelberg, July 1966.
[4] J. D. Fox, C. F. Moore and D. Robson: Phys. Rev. Lett., 12, 198 (1964).
[5] J. D. Anderson and C. Wong: Phys. Rev. Lett., 1, 250 (1961).
[6] A. M. Lane: Nucl. Phys., 35, 676 (1962).
[7] J. B. French and M. H. MacFarlane: Nucl. Phys., 26, 168 (1961).
[8] E. P. Wigner: Phys. Rev., 51, 106 (1937).
[9] D. Robson: Phys. Rev., 137, B 535 (1965); Intern. Conf. Progress Nucl. Phys. with
Tandems, Heidelberg, July 1966.
[10] See for instance, H. A. Weidenmuller : Nucl. Phys., 85, 241 (1966); and A 99, 269,
289 (1967); Proc. S.I.F., Course XL, Varenna (1967), p. 780; R. H. Lemmer: Proc.
S.I.F., Course XL, Varenna (1967), p. 445; see also T. Tamura: Phys. Rev., 185,
1256 (1969).
[11] A. F. R. de Toledo Piza and A. K. Kerman: Ann. Phys., 43, 363 (1967); A. K. Ker
man and A. F. R. de Toledo Piza: Ann. Phys., 48, 173 (1968); see also A. M. Lane:
Isospin in Nuclear Physics, Editor D. H. Wilkinson, NorthHolland, Chapt. 11,
p. 511 (1969).
236 R. A. Ricci
[12] D. Robson, J. D. Fox, P. Richard and F. C. Moore: Phys. Lett., 18,86(1965).
[13] C. F. Moore and G. E. Terrell: Phys. Rev. Lett., 16, 804 (1966).
[14] The first experiment of this type was done by C. F. Moore, L. J. Parish, P. von
Brentano and S. A. A. Zaidi: Phys. Lett., 22, 616 (1966) following the original sug
gestion of G. A. Jones, A. M. Lane and G. C. Morrison: Phys. Lett., 11, 129 (1964).
See also the recent work of P. von Brentano et ah: Phys. Lett., 26 B, 666 (1968)
and of S. A. A. Zaidi et ah: Phys. Rev., 165, 1312 (1968).
[15] P. Richard, C. F. Moore, D. Robson and J. D. Fox: Phys. Rev. Lett., 13, 343 (1964),
[16] G. A. Keyworth, G. C. Kyker, E. G. Bilpuch and H. W. Newson: Nucl. Phys..
89, 590 (1966).
[17] R. A. Ricci: Proc. Intern. Conf. Progress Nucl. Phys. with Tandem, Heidelberg,
1966; G. Chilosi, R. A. Ricci and G. B. Vingiani: Phys. Rev. Lett., 20, 159 (1968);
G. B. Vingiani, R. A. Ricci, R. Giacomich and G. Poiani: Nuovo Cimento, 57,
453 (1968).
[18] G. B. Vingiani, G. Chilosi and W. Bruyensteyn: Phys. Lett., 26 B, 285 (1968),
[19] K. W. Jones, J. P. Schiffer, L. L. Lee, A. Marinov and J. L. Lerner: Phys. Rev..
145, 894 (1966).
[20] P. Wilhjelm, G. A. Keyworth, J. C. Browne, W. P. Beres, M. Divadeenam, H. W.
Newson and G. E. Bilpuch: Phys. Rev., 177, 1553 (1969).
[21] G. A. Keyworth, G. C. Kyker, H. W. Newson and E. G. Bilpuch: Bull. Amer.
Phys. Soc., 12, 585 (1967).
[22] J. C. Browne, G. A. Keyworth, D. P. Lindstrom, J. D. Moses, H. W. Newson
and E. G. Bilpuch: Phys. Lett., 28 B, 26 (1968).
[23] C. Bloch and J. P. Schiffer: Phys. Lett., 12, 22 (1964).
[24] E. Kashy, A. Sperduto, H. A. Enge and W. W. Buechner: Phys. Rev., 135 B, 865
(1965).
[25] W. Beres and M. Divadeenam: Nucl. Phys., 117, 143 (1968).
[26] P. M. Endt: Nuclear Structure (NorthHolland Publ., Amsterdam, 1967).
[27] G. M. Temmer: Proc. Intern. Conf. Nucl. Struct., Dubna, 1968.
[28] D. D. Watson, J. C. Manthuruthil and F. D. Lee: Phys. Rev., 164, 1399 (1967).
[29] S. Maripuu: Nucl. Phys., A 123, 357 (1969).
[30] I. Fodor et ah: Nucl. Phys., A 116, 167 (1968).
[31] R. Giacomich, I. Lagonegro, R. A. Ricci and G. B. Vingiani: to be published.
The Crab Nebula.
Ancient History and Recent Discoveries. (*)
B. B. Rossi
Center for Space Research, M.I.T.  Cambridge, Mass.
1.  The Chinese and Japanese chronicles for the year 1054 of the Chris
tian era registered the sudden appearance in the constellation of Taurus of
a new star — a « guest star » — of extraordinary brightness, which gradually
faded away until, some two years later, it was no longer visible.
Centuries went by, and hardly anyone was aware of this event when, in
1771, the French astronomer Messier compiled a catalogue of all known
cometlike objects (nebulae and clusters) that appeared to occupy fixed
positions in the sky. The first item on his list (Ml) was a nebula in the
constellation of Taurus, about 4 arc minutes across, whose existence had
been known for about 40 years. During the following decades this nebula
was observed repeatedly with improved telescopes. In 1848 the shape of the
object suggested to the British astronomer Lord Ross the name of Crab
Nebula, which has been since generally accepted.
The next event of crucial importance for the present story was the detection
at a Baltic observatory, in 1885, of an exceedingly bright star in the Andro
meda galaxy, that was the result of a sudden flare up. In the subsequent
years, a number of similar stellar outbursts were observed in external gal
axies. In some cases the brightness of the « new » star was comparable to
or even greater than the total brightness of the galaxy before the outburst.
By 1920, it had become generally accepted that these extraordinary out
bursts were not limiting cases of ordinary novae, but were to be regarded
as an entirely different class of astronomical events. Since the late thirties
these events have been known as supernovae.
The discovery of supernovae in external galaxies stimulated the interest
of astronomers in the historical records of events that might be interpreted
(*) This work was supported in part by the National Aeronautics and Space Admin
istration under grant NGR 22009015.
238
B. B. Rossi
as supernovae outbursts within our own galaxy, and prompted them to search
for celestial objects that might be regarded as remnants of these outbursts.
In the early twenties astronomers noticed the coincidence between the posi
tion of the Crab Nebula and the position of the « guest star » of 1054, as
could be deduced from the descriptions contained in the oriental chronicles.
They also discovered that the angular dimensions of the Crab Nebula were
gradually increasing. Under the assumption that the nebula had originated
from a pointlike object and had undergone uniform expansion since its birth,
it was possible to compute its age, which turned out to be close to the time
elapsed since the appearance of the « guest star ». On the basis of these
results Hubble, in 1928, suggested that this event had been a supernova out
burst, and that the Crab Nebula was its remnant.
In the following years the very powerful optical telescopes which by then
had become available were applied to a systematic study of the Crab. It was
Fig. ].  a) Picture of the Crab Nebula in « white light » (taken through a po
laroid filter), showing the diffuse luminosity.
The Crab nebula. Ancient history and recent discoveries
239
found that this object consisted of an « amorphous mass », in which long
and thin « filaments » were embedded. The light from the « amorphous
mass» (which accounted for over 90% of the whole optical emission from
the Crab) had a continuous featureless spectrum. In the light from ihc fila
ments, on the other hand, the lines of the known elements (especially the
Hat line of hydrogen) appeared prominently (see Fig. I).
Fig. I,  h) Picture of the Crab Nebula in Hx {taken through an interference
filler).* showing Ihc filamentary structure (Mt. Wilson and Paloniar Observatories).
The spectral lines of individual filaments were observed to exhibit Doppler
shifts, which were interpreted as due to the expansion of the nebula. From
this effect, the radial component of the velocity of expansion was found to
be a little over 1000 km/s. This result together with the observed rate of
increase of the angular radius (0.21 arc s/y) provided an estimate of 5000
240 B. B. Rossi
light years for the distance of the Crab Nebula, under the assumption that
the velocities of expansion along the line of sight and perpendicularly to it
were identical. (However, it is now believed that the expansion may not be
exactly isotropic, and consequently that the above estimate of the distance
may be in error by some 20%, probably on the low side.)
In the meantime, theoretical ideas pertinent to the supernova phenom
enon began to emerge. Already in 1939 Oppenheimer and his collaborators
addressed themselves to the problem of what happens when the nuclear fuel
in the central part of a star is nearly exhausted, so that the pressure of the
radiation generated by the nuclear reactions can no longer balance the forces
of gravitational attraction. They found that, depending on its mass, the star
will collapse either into a « white dwarf », or into a lump of nuclear matter,
i.e., a « neutron star ». According to present views , prior to the final collapse,
part of the stellar mass is blown out into space, perhaps because of the sudden
ignition of the remaining nuclear fuel. This outburst manifests itself as a
supernova, and the ejected matter forms the cloud later found at the location
of the outburst.
By then, astronomers had discovered two faint stars near the center of
the Crab Nebula, and had suggested that either of them might be the residual
condensed object of the supernova explosion of 1054. However, while one
of these stars had an entirely « normal » spectrum, the other (known to the
astronomers as the south preceding star) was found to have a featureless
spectrum, quite different from the spectra of ordinary stars. Furthermore,
for some time astronomers had been observing certain peculiar « ripples »,
which traveled through the cloud at enormous speed (about r the speed of
light). Careful measurements showed that the vector velocities of these
ripples were directed away from the south preceding star. For both these
reasons Baade and Minkowsky in 1942 concluded that this object rather than
the other member of the doublet should be identified as the supernova remnant.
2.  Astronomical research in the years following the end of the second
world war was dominated by the almost explosive development of radio
astronomy. One of the first discrete radio sources to be identified with an
optical object was the Crab Nebula [1].
The discovery of the radio emission of the Crab brought to a sharper
focus the problem of the origin of the radiation from this object, which had
puzzled astronomers for several years. Indeed, while it had been found very
difficult to explain the shape and the intensity of the optical continuum in
terms of thermal processes (the only celestial radiation processes well under
stood at the time), in no way could processes of this kind account for the
strong radio signals.
The Crab nebula. Ancient history and recent discoveries 241
The solution of the problem came in the early fifties when Shklovsky
suggested that both the radio emission and the optical continuum were due
to the same, nonthermal process, a process to be identified with the socalled
synchrotron effect, i.e., the emission of electromagnetic radiation by highly
relativistic electrons traveling in a magnetic field [2]. Unlike thermal radiation,
synchrotron radiation is linearly polarized. Although it was difficult to pre
dict whether or not a polarization might actually be observable (since in
the case of a source of finite dimensions the net effect depends on the degree
of randomness of the magnetic field), Shklovsky's suggestion prompted astron
omers to search for a polarization of the optical continuum of the Crab.
The positive results of these observations, and the detection, some time later,
of a similar polarization in the radio band of the spectrum, have been generally
accepted as a crucial test of the synchrotron hypothesis. Today, of course,
the synchrotron process is known to play a major role in many astrophysical
phenomena. But it is worth noting that it was in the Crab Nebula that the
occurrence of this process on a cosmic scale was first established.
Synchrotron emission extending into the optical band implies that the
Crab Nebula is permeated by a magnetic field (of an estimated strength
between 10 4 and 10~ 3 G) and contains electrons with energies extending
up to at least 10 12 eV. Various suggestions about the origin of these electrons
were put forward (although none was worked out quantitatively into a theory).
Highenergy electrons might have been left over from the original explosion;
or they might be ejected continuously from the central star; or they might
be accelerated while moving through the cloud by some sort of Fermitype
process. Whatever mechanism was responsible for the acceleration of elec
trons, it was thought that the same mechanism would also accelerate protons
and heavier nuclei. While the electrons lost their energy (or most of it) within
the cloud by synchrotron emission, protons and heavier nuclei (for which
synchrotron losses are negligible) would escape into interstellar space without
appreciable energy loss, and would thus contribute to the galactic cosmicray
flux. In fact, it was argued that all galactic cosmic rays may originate from
supernovae, being produced primarily at the time of the initial outburst.
3.  In 1962, the discovery of surprisingly strong celestial sources of
Xrays — including both localized sources and a diffuse background [3] —
opened up the new field of Xray astronomy. Xrays, of course, can only
be observed at very high altitudes, because of their strong absorption in
the atmosphere. Most of the results available to this date have been obtained
by means of rockets, although balloons have made important contributions
to the study of the « hard » component of the Xray flux. The second Xray
rocket, flown in October 1962 [4] already gave some tentative indication
16
242 B. B. Rossi
of an Xray source in the general direction of the Crab Nebula. The follow
ing spring a rocket equipped with a detector of improved angular resolution
established the existence of an Xray source within a few degrees of the
Crab [5]. The crucial proof that this source was indeed coincident with the
Crab came in the summer of 1964 when a rocket flown during an eclipse
of the Crab by the moon showed the simultaneous disappearance of the
Xray and of the optical flux [6], The identification was confirmed in 1967
by means of a collimator of very fine angular resolution, which measured both
angular coordinates of the Xray source with a precision of about 20 arcs [7].
The results of the 1964 and 1967 observations are summarized in Fig. 2.
They agree in showing that, within the observational uncertainties, the center
of the Xray source is coincident with the center or the visible nebula. More
over both experiments indicate that the Xray source is not pointlike, but
NRL (MANLEY 1965)
zrss'w
Fig. 2.  Observational results on the location and size of the Xray source in
the Crab Nebula, superimposed on a photograph of the nebula in ordinary
light [7]. The data were obtained by Bowyer et at, [61 who observed the occult
ation of the Crab by the moon, and by Oda el at. [7], using a modulation col
limator. The arc marked «NRL 1964 » shows the position of the moon's limb
at the time when it crossed the center of the Xray source, as given by Bowyer
et af. The arc marked «NRL (Manley 1965) » shows the same data, corrected
for the motion of the rocket during the experiment [31]. The intersection of the
« prerotl» and « postroll» lines is the most likely position of the center of the
source, as determined by Oda et a!.\ the observational errors of this determi
nation are also indicated. The dotted circle represents the approximate dimen
sions of the Xray source.
The Crab nebula. Ancient history and recent discoveries 243
has an angular diameter of about 100 arcs {i.e., of the same order as that
of the visible nebula, although perhaps somewhat smaller).
Since its discovery, the Xray source in the Crab has been the object of
many observations. In reporting the results of these observations, it may be
instructive to compare them with those concerning another strong Xray
source, ScoX1, which has also been extensively investigated. Unlike the
Crab, Sco Xl had not been recognized by the astronomers as a peculiar
celestial object before its discovery as an Xray emitter. Subsequently it was
identified with a faint star of unusual spectral characteristics [8]. Again
unlike the Crab, Sco Xl appears pointlike (to the limit of the resolution
achieved so far) both in the optical and in the Xray band.
The Xray emission from the Crab, as well as its light emission, were
found to be nearly constant in time, at least when averaged over periods of
seconds (Sco Xl, on the contrary, was found to be highly variable both in
the Xray and in the optical bands).
In the Xray band, the spectral function of the Crab (energy flux per unit
interval of photon energy) was found to follow closely a power law with expo
nent close to unity from hv=l keV to A^=100keV. (The Xray spectrum
of Sco Xl has a very different shape, being represented approximately by
an exponential function, similar to that expected from a thermal, optically
thin source at about 5xl0 7 °K. This implies that the spectrum of Sco Xl
is much « softer » than that of the Crab; indeed, while Sco Xl is about
10 times brighter than the Crab at photon energies of the order of 5 keV,
the Crab becomes brighter than Sco Xl at photon energies above about
30 keV.)
A loglog plot of measurements in the radio, visible, ultraviolet, and Xray
bands suggests that the whole electromagnetic spectrum of the Crab may
be described by a single smooth function. This has been taken as an argu
ment in favor of a common origin (i.e., synchrotron radiation) for the entire
spectrum. Although not yet definitely proven, the assumption of a synchro
tron origin for Xray spectrum of the Crab is accepted by most scientists,
to a large extent because of the difficulty of finding a more likely alternative.
The only other process that has been considered seriously is thermal radiation
from a hot, optically thin plasma cloud. As already noted, if the cloud is
at a uniform temperature, this process gives rise to an exponential spectrum,
i.e., a spectrum more similar to that of Sco Xl than to that of the Crab.
Of course, if the plasma temperature varies from point to point, as it may
well do in the Crab Nebula, the Xray spectrum will be a sum of exponentials
which might conceivably simulate a power law over a limited range of photon
energies. However, beyond a photon energy corresponding to the temper
ature of the hottest region, the spectrum should drop sharply. Therefore
244 B. B. Rossi
the possibility of a thermal radiation process became increasingly remote as
spectral measurements were extended to higher and higher energies and
failed to detect any cutoff.
With the magnetic fields that supposedly exist in the Crab, synchrotron
emission in the Xray band requires electron energies of the order of 10 14 eV.
It is worth noting that for these very energetic electrons the synchrotron
process is exceedingly effective. Consequently the electrons lose energy at
a very fast rate, which appears to rule out the possibility that they might
have originated from the initial explosion.
At this point it may be useful to quote some figures. The Xray flux
from the Crab Nebula, in the spectral band from hv = 1 keV to hv=l00 keV,
amounts to about 7 x 10~ 8 erg/cm 2 s at the earth. Taking the distance
of the Crab as 5000 l.y., its Xray emission turns out to be about 2xl0 3r
erg/s, i.e., about 5000 times the total emission of the Sun in all wavelengths.
The emission in the optical band is about \ and the emission in the radio
band (A>3cm) is about 1/1000 of the Xray emission. (For ScoX1, the
corresponding figures are about 1/1000 and about 2xl0 8 .)
4.  We now come to the very recent developments of astronomical
research, and here again we find that the Crab Nebula occupies a central
position in the new discoveries.
Early in 1968, Hewish and his coworkers announced the discovery of
pulsating radio sources, or pulsars [9]. At the end of that year, some 25
pulsars were known, with periods ranging from about 2 to 1/30 s. Of these,
only two had been identified with previously known celestial objects, both
of them supernova remnants. One of them was Vela X [10] the other was
the Crab Nebula [11]. The pulsar in Vela X had a period of about 89 ms,
that in the Crab (known also as NP 0532) had a period of about 33 ms,
the shortest among all known pulsars.
The periods of the « slow » pulsars were found to be remarkably constant
(for some of them it was established that the rate of change was less than
one part in 10 8 per year). The periods of the « fast » pulsars in Vela X and
the Crab, on the other hand, were found to increase very slowly. For the
Crab, the rate of increase amounts to one part in 2400 per year (*).
In January 1969 another important discovery took place, with the detection,
in the Crab Nebula, of the first and thus far the only optical pulsar [14].
The period of the optical pulsations was found to be exactly identical to that
of the radio pulsations, which proved beyond any reasonable doubt that the
(*) In the case of Vela X, the gradual increase of the period was interrupted, between
February 4 andh March 3, 1969, by a sudden decrease of two parts in one million [12, 13].
The Crab nebula. Ancient history and recent discoveries
245
Fig. 3.  Siroboscopic pictures of the stars near the center of the Crab Neb
ula taken by J. S Miller and E. I. Wamplcr at the Lick Observatory. The
pulsar appears as the brightest object in the picture at the top; it is nearly in
visible in the picture at the bottom. The change in the apparent brightness is
due to the gradual phase change of the light pulses relative to the « open pe
riods » of the stroboscope disk [16] (Lick Observatory photograph).
246 B. B. Rossi
radio and the optical pulsars were the same object (although, of course, the
radiations belonging to the two spectral bands may come from different
regions of this object). Precise determinations of its position showed that
the pulsating star is the south preceding member of the doublet found near
the center of the Crab [15], and thus confirmed unequivocally the previous
tentative identification of this star as the condensed residue of the supernova
explosion. A further dramatic verification of this result came from a series
of photographs taken through the slots of a rotating disk, which showed
that the brightness of the south preceding star changed periodically between
a maximum and practically total extinction when the time between successive
« open » intervals was nearly equal to the period of the pulsations (see Fig. 3).
Quite naturally, the discovery of the optical pulsar in the Crab suggested
a search for a pulsating component in the Xray emission of the same object.
During the month of April 1969, two rockets provided with detectors sensitive
to « soft » Xrays (photon energies of several keV) were launched for this pur
pose, the first by the NRL group [17], the second by the MIT group [18].
Both experiments did, in fact, detect the expected pulsations, with a
period exactly equal to that of the radio and of the optical pulsations
(33.099522 ms at the time of the MIT flight).
Finally, a recent analysis of balloon data obtained in 1967 revealed that
also the « hard » Xray flux of the Crab (photon energies greater than about
35 keV) contains a pulsating component [19]. A balloon flight carried out
in May 1969 confirmed this result and provided quantitative information
on the size and shape of the pulses [20].
Examples of the pulse shapes observed in different spectral bands appear
in Figs. 47. Shown in each case is the time dependence of the radiation flux
during one period, averaged over a large number of periods.
One sees that, at all wavelengths, each pulse contains two peaks, sepa
rated by a time interval slightly less than one half the period. In the optical
and in the Xray bands, the shape of the pulses appears to be quite constant.
In the radio band, however, the pulse shape varies greatly from pulse to
pulse, and even averaging over thousands of pulses does not result in a stable
pattern. It has been pointed out that this instability may be due, at least
in part, to refraction of radio waves, possibly in the ionized gases within the
nebula itself [23, 24]. This interpretation is consistent with the observed sta
bility of the optical and of the Xray pulses because refraction effects decrease
rapidly with decreasing wavelengths.
There is evidence that at all wavelengths the radiation level between the
first and the second peak is somewhat higher than the radiation level after
the second peak. We shall take the view that this lowest level of radiation
represents the steady emission of the nebula. In other words we shall assume
The Crab nebula. Ancient history and recent discoveries
247
that the emission of the pulsar actually drops to zero during each period.
(Stroboscopic pictures such as those shown in Fig. 3 tend to support this
assumption, but do not prove that it is rigorously correct.) By taking the
lowest radiation level as the zero line, we can then separate the pulsating
component of the radiation originating from the pulsar, from the steady
component originating from the nebula.
10 ms
10ms
Fig. 4.  Average pulse shapes of the pulsar in the Crab Nebula, as observed
on three different days and at three different radio frequencies with the 1000 ft
antenna at the Arecibo Ionospheric Observatory; a) Nov. 14, 1968; 196.5 MHz;
18000 pulses, b) Nov. 26, 1968; 198 MHz; 21 153 pulses, c) Dec. 2, 1968;
430.0 MHz; 53 427 pulses [21].
248
B. B. Rossi
7,000
•"■ " ' t
1 1—
— i 1
1 r
6,000
■
■
5,000

4,000
a

3,000
."
".__
/
■
2,000
'' : r>.».^,.
•.•..v.v/.w.''"
^,,0^,;^,,..
,,,v,,...
.'
b

"'•"..,.._....._.... .

250
ab

'
i '. L 1_
1 1
, •'••."■•'■:"
75 100 125 150 175 200 225 250 275
Fig. 5.  Light curves for the Crab pulsar in white light, a) sum of 100000 pe
riods; b) sum of 30000 periods, taken 3 J h earlier. The abscissa is channel
number, each channel being of 100 \xs duration; the lefthand scale refers
to curve a) and the righthand scale to curve b) [22].
Observations show that the ratio between the power in the pulsating
mode and the power in the steady mode varies by a very large factor over
the spectrum. In the radio and in the optical bands this ratio amounts to
only several parts in one thousand. In the « soft » Xray band it reaches
the value of about 9 % and in the « hard » Xray band it seems to be higher
still. From these results and from the spectral data on the total emission
of the Crab reported previously it follows that all but a minute fraction
(perhaps less than 1 %) of the radiation from the pulsar is in the form of
Xray. This object, then, may be properly described as an Xray pulsar.
The pulses observed in the optical and the Xray bands, while very dif
ferent in their size relative to the steady component, have strikingly similar
shapes. In both spectral bands, one of the two peaks observed during each
period has a width of about 1.5 ms, and the other has a width of about
3.5 ms (*). Within the experimental errors, the separation of the two peaks
(*) However, one should note that the observed width of the narrow Xray peak is
not much greater than the time resolution of the instrument.
The Crab nebula. Ancient history and recent discoveries
249
(0) XRAYS
8000 h fil
o
o
a.
0)
7000 
6000 
4.5% »
13 3 msec f
A
4>6%
7490
counts
IT
Primary
Optical
Peak
I"
4i
B
counts _ ^J
_[b) Optical
33,099,522 nsec
Fig. 6.  a) «Soft» Xray data for the Crab pulsar obtained during 150 s
of the rocket flight carried out by Bradt and his coworkers on April 27, 1969.
The detector was sensitive to photons in the energy range from 1.5 to 10 keV.
Data were superimposed by dividing each period into 40 equal « bins » and
distributing the counts into these bins. The intensities represented by the areas
under peaks A and B are 4.5% and 4.6%, respectively, of the total Xray in
tensity from the Crab, b) Optical data shown in Fig. 5, integrated into 41 « bins »
for comparison with the Xray data [18].
is the same (about 13.5 ms). In the experiment by Bradt and his coworkers
(see Fig. 6) recording of time signals from the WWV radio station during
the rocket flight made it possible to correlate the Xray observations with
optical observations carried out, within a few hours of the flight, at the Mc
Donald Observatory and at the Palomar Observatory. It was thus shown
that the narrow peaks in the Xray and in the optical bands are simultaneous
within 1 ms.
250
B. B. Rossi
20 200 
c 20 000 h
m
w.
° 19 800 h
o
u
19 600 
19 400
I4±ms
2941
counts
I—  u,
I I I I I I t I I I I I I I I I I I I I I I I I I
I 3 5 7 9 II 13 15 17 19 21 23 25 27 29
Bin Number
Fig. 7.  « Hard » Xray data for the Crab pulsar obtained during the balloon
flight of May 10, 1969 by Floyd and his coworkers. The measurements cover
the energy range from 25 to 100 keV. The data are divided into 30 « bins » [20].
The great variability of the radio pulses denies the possibility of a detailed
comparison of their shape with that of the optical and radio pulses. Further
more, the wavelengthdependent delay of the radio pulses due to dispersion
in the interstellar medium makes it difficult to establish an exact time cor
relation between the radio peaks and the optical peaks. All one can say
on the basis of published reports is that the peaks in the radio and optical
bands are simultaneous, with an uncertainty of about 6 ms, due almost
entirely to the interstellar dispersion [25].
5.  A reliable theoretical interpretation of the observational data that
have been described above is still lacking. From these data, however, there
begins to emerge a model which, although tentative and incomplete, may be
worth discussing.
When pulsars were first discovered, two different kinds of models were
suggested to account for their equallyspaced signals; i.e., a) vibrational
models and b) rotational models. The vibrating or rotating star was thought
to be either a) a white dwarf or b) a neutron star. While it was difficult to
discriminate between these various possibilities as long as only pulsars with
periods of the order of a second were known, the discovery of pulsars with
periods of less than 0.1 s practically eliminated all choices but one. Since
the free oscillations of white dwarfs have periods considerably longer than
The Crab nebula. Ancient history and recent discoveries 251
0.1s; since white dwarfs cannot rotate at 10 rps or more without being
disrupted; since the free oscillations of a neutron star are believed to be
rapidly damped through the production of gravitational waves, it became
practically certain that pulsars (or at least the « fast » pulsars such as that
in the Crab Nebula) were rotating neutron stars.
We can estimate the kinetic energy of rotation E of the pulsar in the
Crab by assuming that its mass is of the order of one solar mass (~ 2 x 10 33 g)
and by taking the conventional value of 10 km for its radius. With the
observed angular velocity of 27zx30^ 190 s _1 we obtain
E^ 1.4xl0 49 erg.
From this figure and from the observed rate of increase of the period it
follows that the pulsar loses rotational energy at the rate
dF
— ~ t*t 3.7 xlO 38 ergs^ 1 .
at
From the data reported previously we may estimate the total energy of the
electromagnetic radiation of all frequencies emitted by the Crab Nebula to
be several times 10 37 erg s _1 . It seems likely that an amount of energy,
perhaps of the same order of magnitude, may be spent by the Crab Nebula
in the production of cosmic rays. Thus, within the large uncertainties of
the present estimates, — dE/dt appears to be remarkably close to the total
energy output of the Crab Nebula, which naturally suggests that this energy
is supplied the gradual slowing down of the rotating neutron star at the center
of the Crab [26, 27]. An additional justification for accepting this suggestion
as a working hypothesis in the formulation of our model may be found in
the fact that previously it had been necessary to resort to ad hoc assumptions
in order to account for the energy storage in the Crab Nebula.
It appears natural to interpret the pulsating signals received from a rotat
ing object as due to a lighthouse effect [28]. As another working hypothesis,
we shall therefore assume that the electromagnetic radiation from a neutron
star is confined to one or more narrow beams, which sweep past the observer
as they corotate with the star. In the case of the Crab, there would be at least
two such beams. The narrow principal peak requires a beam whose angular
width in the direction perpendicular to axis of rotation is at most 2tz/20 (less
if the axis of rotation is not perpendicular to the line of sight.) If this beam
were in the shape of a circular cone, the a priori probability of its being de
tected by an observer on the earth would be 5% or less. Similarly the prob
ability of detecting the beam responsible for the wider pulse would be 10 %
252 B. B. Rossi
or less. We conclude that either the earth is in a peculiarly favourable po
sition for the observation of the signals from the pulsar in the Crab ; or the
beams responsible for these pulses are fanshaped rather than circular; or
there are more than two beams.
The emission of the radiation into discrete beams implies an azimuthal
anisotropy in the structure of the pulsar with respect to its spin axis. The
stability of the beams as observed in the visible and Xray bands is more
easily understandable if the anisotropy is due to a magnetization of the pulsar
rather than to « hot spots » or other peculiarities in a plasma atmosphere
of the pulsar, as had been suggested when only radio observations were
available [28]. It should be noted that the collapse of a star with a moderate
magnetic field will, indeed, result in a neutron star with exceedingly large
magnetization, even if only a minor fraction of the original magnetic flux
is conserved. (For a star similar to the Sun, 100% flux conservation would
give rise to fields of the order of 10 9 G at the surface of the neutron star;
field strengths up to 10 13 G have been mentioned as a possibility.) It thus
appears reasonable to further specify our model by assuming that the neutron
star is strongly magnetized, and that the magnetization is not axially symmetric
with respect to the spin axis.
We now come to the problem of the processes responsible for the steady
component of the radiation (originating from the nebula) and of the pulsat
ing component (originating from the neutron star). With regard to the former,
as already noted, we know for sure that the continuous spectrum extending
from the radio waves to the ultraviolet is due to a synchrotron effect, and we
have good reasons to believe that the same effect is also responsible for the
Xray emission ; which means that the nebula contains electrons with energies
up to at least 10 14 eV. According to our model, these electrons derive their
energy from the kinetic energy of rotation of the neutron star. We may think
of a direct process, whereby the electrons are accelerated by the strong time
varying electromagnetic field that exists in immediate neighborhood of the
star, and are then injected into the surrounding magnetized plasma cloud.
Alternately, we may think of an indirect acceleration mechanism; i.e., we may
assume that the rotating neutron star loses energy to the cloud giving rise to
disturbances (in the form of waves or shocks), which then, through a Fermi
type stochastic interaction with the electrons in the cloud, supply the energy
radiated via the synchrotron process.
An analysis of the stochastic acceleration process (for example on the
basis of a model based on the interaction between Alfven waves and individual
electrons [29]) shows that the high efficiency needed to maintain the required
electron spectrum can be achieved only under rather extreme circumstances.
On the other hand, no quantitative treatment of the direct acceleration
The Crab nebula. Ancient history and recent discoveries 253
process has yet been developed. In this connection one should keep in mind
that the electrons will lose energy by synchrotron radiation even as they
are accelerated ; and that the synchrotron losses are proportional to the square
of the magnetic field and to the square of the energy. Therefore it is not
easy to figure out how electrons can emerge from the region of strong ma
gnetic field surrounding the neutron star with the enormous energy they need
to radiate Xray photons in the weak field of the nebula.
Let us consider next the pulsating component of the radiation. One may
think of a variety of processes capable of generating pulsations in the long
wavelength band of the spectrum. The fundamental problem, however, is
to explain the emission in the Xray band which, by itself, accounts for at
least 99 % of the pulsating power, as already noted. In this portion of the
spectrum, it appears that the only effective emission process is the inter
action of electrons with the magnetic field. This process presupposes the
existence around the neutron star of electrons with a suitable energy distri
bution. In the frame of reference corotating with the star, the spacial
distribution of the electrons must be remarkably stable; i.e., the electron
cloud must corotate rigidly with the star. Furthermore, the distribution of
the electrons in velocity space, and the pattern of magnetic field lines, must
be such as to account for the required beamshaped emission.
Of course, rigid corotation can only occur up to a maximum distance of
the spin axis where the rotational velocity becomes equal to the velocity of
light [28]. With an angular velocity of 190 s~\ this distance amounts to
1.6xl0 8 cm. Note that, if the magnetic field resembles that of a dipole,
and therefore varies as the inverse cube of the distance, its magnitude at
the « light circle » in the equatorial plane is about 2.5 x 10 4 times smaller
than at the surface of the neutron star.
Of course, electrons require a much smaller energy to radiate Xray
photons in the strong magnetic field surrounding the neutron star than they
do in the weak magnetic field of the cloud. In this connection it is important
to keep in mind that the motion of electrons in the plane perpendicular to
the magnetic field is actually quantized [30]. In the subrelativistic region
the energy levels are equidistant with a separation Ae = hco/2ji, where co
is the cyclotron frequency. With Ae measured in eV and the magnetic
field B in gauss, the following relation holds
Ae = 1. 16xl0 8 B.
If Ae is very small compared with the photon energy, quantum effects are
negligible and the interaction of the electrons with the magnetic field may
be described by the classical theory of magnetic bremsstrahlung. In this
254 B. B. Rossi
case the average energy of the radiated photons is much smaller than the
electron energy. If, however, Ae is close to the photon energy then the
emission occurs via a process similar to an atomic quantum transition between
two bound levels, and the energy of the emitted photons is equal to or a
sizeable fraction of the electron energy. Even hard Xray photons, then, may
be produced by subrelativistic electrons.
Quantized emission in the Xray band requires magnetic fields of the
order of 10 12 G or more. While these fields are not ruled out, it appears
more likely to the author that Xrays are produced in a region of lower
magnetic field, in which case relativistic electrons are needed. One must then
assume that electrons are first accelerated to relativistic, but not necessarily
extremely high, energies by the rotating neutron star. While in the vicinity
of the star, they partake of its rotation and generate the pulsating component
of the radiation. They then diffuse into the surrounding cloud, where, after
perhaps gaining further energy, they give rise to the steady radiation.
6.  To summarize, the model developed here pictures the Crab
Nebula as a thin plasma cloud containing a weak magnetic field, with a fast
rotating, stronglymagnetized, neutron star at its center. The magnetization
of the star does not have axial symmetry with respect to the spin axis, so
that the rotation gives rise to timevarying electromagnetic fields, which,
in some way or another, are capable of accelerating electrons. For a while
these electrons remain within the corotating magnetosphere of the neutron
star, where they give rise to corotating beams of electromagnetic radiation.
Subsequently they diffuse into the surrounding cloud, where perhaps they
acquire further energy by a Fermitype stochastic process. Synchrotron
emission by these electrons in the weak magnetic field of the cloud gives
rise to the steady flux of radiation.
Presumably the kinetic energy of rotation of the neutron star was initially
derived from the conversion of some fraction of the gravitational energy
released during the stellar collapse following the supernova explosion. From
the time of its birth, the Crab Nebula has drawn from the rotating neutron
star the energy needed to produce the various kinds of rays which it has been
pouring out into space.
Whether or not the general features of this model will survive future
observations and future theoretical discussions is still an open question.
Here the model is presented as a working hypothesis, that may be useful in
suggesting further lines of investigation. From the theoretical point of view,
one of the basic problems is clearly a quantitative analysis of the possible
mechanisms for the acceleration of the electrons. From the observational
point of view, it would be desirable to examine the polarization of the Xray
The Crab nebula. Ancient history and recent discoveries 255
emission in order to test the assumption that it originates from a synchrotron
process. Furthermore it would be very illuminating to extend the obser
vations of the steady and of the pulsating components of the electromagnetic
spectrum to considerably higher photon energies. Finally we may hope that
highresolution Xray pictures of the Crab, possibly taken at different wave
lengths, will furnish important information on the mechanism responsible
for the acceleration of electrons and help discover the region of space where
this acceleration occurs.
REFERENCES
[1] J. Bolton and G. Stanley: Aust. J. Sci. Res., A 2, 139 (1949).
[2] I. S. Shklovsky: A. Zh., 30, 15 (1953); D.A.N. , 90, 983 (1953).
[3] R. Giacconi, H. Gursky, F. R. Paolini and B. Rossi: Phys. Rev. Lett., 9, 439 (1962).
[4] H. Gursky, R. Giacconi, F. R. Paolini and B. Rossi: Phys. Rev. Lett., 11, 530 (1963).
[5] S. Bowyer, E. T. Byram, T. A. Chubb and H. Friedman: Nature, 201, 1307 (1964).
[6] S. Bowyer, E. T. Byram, T. A. Chubb and H. Friedman: Science, 146, 912 (1964).
[7] M. Oda, H. Bradt, G. Garmire, G. Spada, B. V. Sreekantan, H. Gursky, R. Giac
coni, P. Gorenstein and J. Waters: Ap. J., 148, L5 (1967).
[8] A. R. Sandage, P. Osmer, R. Giacconi, P. Gorenstein, H. Gursky, J. Waters,
H. Bradt, G. Garmire, B. V. Sreekantan, M. Oda, K. Osawa and J. Jugaku:
Ap. J., 146, 316 (1966).
[9] A. Hewish, S. J. Bell, J. D. H. Pilkington, P. F. Scott and R. A. Collins: Nature,
217, 709 (1968).
[10] M. I. Large, A. E. Vaughan and B. V. Mills: Nature, 220, 340 (1968).
[11] D. H. Staelin and E. C. Reifenstein: Science, 162, 1481 (1968).
[12] V. Radhakrishnan and R. N. Manchester: Nature, 222, 228 (1969).
[13] P. E. Reichley and G. S. Downs: Nature, 222, 229 (1969).
[14] W. J. Cooke, M. J. Disney and D. J. Taylor: Nature, 221, 525 (1969).
[15] R. Lynds, S. P. Maran and D. E. Trumbo: Ap. J., 155, L 121 (1969).
[16] J. S. Miller and E. J. Wampler: Nature, 221, 1037 (1969).
[17] G. Fritz, R. C. Henry, J. F. Meekins, T. A. Chubb and H. Friedman: Science,
164, 709 (1969).
[18] H. Bradt, S. Rappaport, W. Mayer, R. E. Nather, B. Warner, M. Mac Farlane
and J. Kristian: Nature, 222, 728 (1969).
[19] A. J. Fishman, F. R. Harnden and R. C. Haymes: Ap. J., 156, L 107 (1969).
[20] F. W. Floyd, I. S. Glass and H. W. Schnopper: Nature, 224, 50 (1969).
[21] J. M. Comella, V. D. Craft, R. V. E. Lovelace, J. M. Sutton and G. L. Tyler:
Nature, 111, 453 (1969).
[22] B. Warner, R. E. Nather and M. Mac Farlane: Nature, 222, 223 (1969).
[23] P. A. G. Sheuer: Nature, 218, 920 (1968).
[24] O. B. Slee, M. M. Komesaroff and P. M. McCullough: Nature, 219, 342 (1968).
256 B. B. Rossi
[25] E. K. Conklin, H. T. Howard, J. S. Miller and E. J. Wampler: Nature, 111,
552 (1969).
[26] T. Gold: Nature, 111, 25 (1969).
[27] A. Finzi and R. A. Wolf: Ap. J., 155, L 107 (1969).
[28] T. Gold: Nature, 218, 731 (1968).
[29] O. Manley and S. Olbert: Ap. J., 157, 223 (1969).
[30] H. Y. Chiu, V. Canuto and L. FassioCanuto : Nature, 111, 529 (1969).
[31] O. Manley, R. Finn and G. Ouellette: Private communication (1965).
The K L — K s Mass Difference.
C. RUBBIA
CERN  Geneve
1.  Introduction.
The existence of a very small mass difference between the long and the
shortlived components of the neutral K system has been firstly postulated
in the theory of particle mixture of GellMann and Pais [1].
The K and K particles, produced in strong and electromagnetic inter
actions, belong to the isotopic spin doublets (K + , K ) and (K~, Kq) and have
definite hypercharges, +1 and — 1, respectively. Furthermore, as a conse
quence of CPT invariance, particle and antiparticle have identical masses,
i.e., M Ko Mk o .
However, weak interactions do not conserve hypercharge and they can
induce not only decays but also transition between K and Kq. For instance
transitions are mediated to the second order by any common decay chan
nel F, i.e.
K <> F<> K .
After an infinitesimal proper time interval Sf, the hypercharge eigen
states K and K have evolved as follows [2]:
(1)
\Ky>\Kym{M\Ky+ b\k>},
\K> > \K> — i$t{ A\K> + M\K)} .
The (complex) terms A and B, represent the K <> K mixing effects and
M and M are related to the K and Kq masses decay rates:
17
258 C. Rubbia
There exist two definite linear combinations of the \K} and liO states:
(2)
\L> = p\K> + q\K> ,
\Sy = r\K> + s\K> ,
which have simple, uncoupled time evolutions:
\l> > \Ly — i8tM L \L> , \sy > \Sy—i8tM s \S}
and which obviously describe the long and shortlived states of simple
exponential decay observed experimentally. The quantities M L and M s are
defined :
M L = m L — l r L , M s = m s —r s ,
where r L , m L , r s , m s are, respectively, the masses and decay rates of the
long and shortlived states. Relating expressions (1) and (3) with the help
of formula (2) one finds easily:
M = (M L sp — M s qr)/(sp —qr), M= (M s sp — M L qr)/(sp — qr) ,
A =(M s — M L )7tp/(sp — qr), B = (M L —M s )sq/(sp—qr) .
Introducing the condition M = M required by CPT invariance and with
some phase conventions, the above expressions become considerably simple,
since s = — q, r =p:
M=M = ^(M S +M L ),
A = \^{M L M S ), B=^(M L M S ).
The masses of the long and shortlived states are therefore different,
their difference being proportional to the terms A and B. As we have seen,
these terms are originated by K <>K transitions which now give different
contributions to the K L and K s selfenergy diagrams.
A first estimate of the magnitude of Bm = m L — m s is easily obtained
from dimensional considerations [3]. If weak interactions to the first order
satisfy to the rule A»S = 1, it is possible to connect K and K only with
second or higher order diagrams. Consequently Sm is of order (Grsinfl) 2 ,
where Gf is the Fermi constant, and 6 is the Cabibbo angle:
G 2
8w c± ^ sin 2 • m 5 ~ 10~ 5 eV (for m = w K ) .
4?r
The K L — K s mass difference 259
This is of the same order of magnitude of the total K s transition rate,
r s = 1.145 x 1(T s\ equivalent to T s h = 0.58 x lO" 5 eV.
If K <»K transitions occur directly (AS = 2) with strength fG?, the
corresponding mass difference is approximately:
8ra =/G F m 3 ~ 1.2 x 10 3 /eV (for m = m K ) .
Initially the interest in the K L — Kg mass difference has been simply
whether it was of the same magnitude as r s h or much larger. Since the
discovery CP violation in neutral Kdecay [4] it has become important to
know with precision the mass difference.
An accurate knowledge of Sra is at the basis of the phenomenological
analysis of the nature of CP violation in neutral decay. A more accurate
value of Sra is also demanded in the analysis of experiments measuring the
phase of the CP violating amplitude r} + _ = A(K l +k + k)/A(K s >tz + iz).
The most direct way to determine the phase of rj ± is to observe interference
between the K l ^k + k~ and K s >tz + tz~ decay amplitudes close to the pro
duction point of K state [5]. Since \rj + _\ ~ 2x 10~ 3 , such interference effects
are large only relatively far from the production point where the K s amplitude
has decayed down to the »? + _ level: expT g f/2) ~r) + _.
The error in the measured phase then will come to the greatest extent
from the error in Sra which enters in the argument of the interference term
in the form <$m~t, with t~ 12 /r s . This technique is then limited to the accu
racy with which the mass difference is known.
2.  How to measure the mass difference?
Many different tecniques have been employed to determine 8ra, since
the existence of such a mass difference was suggested. All these experiments
show the mass difference as an interference process between a coherent super
position of K L and K s states, the phase difference between the two states
showing a characteristic precession due to the mass difference Sra. The
attractive feature of all these experiments is that the smallness of the K £ — K s
mass difference makes it possible to realize experimental conditions in which
a coherent superposition of K L and K s states can be observed over long times
and over a variety of arrangements. In the present paper we shall consider
only the most recent techniques which almost invariably make use of the
phenomenon of coherent regeneration. Pais and Piccioni [5] first pointed
out the existence of a regeneration process for neutral K mesons but it was
M. L. Good [6] who gave a complete description of this process and the
application of this technique to the determination of Sm. Whenever a beam
260 C. Rubbia
of longlived K meson traverses a slab of material, the « regenerator » because
of difference of strong interaction crosssection for K and K components,
the propagation of the incoming state is modified and a small coherent K s
amplitude is regenerated. Thus the time evolution of the K and K states
instead of (PCT)
\Ky^\K} — iM$t\Ky — iB$t\Ky,
\K> > \K> — iM8t\K> — iA$t\K} ,
we shall have in matter the additional terms due to nuclear absorptions
where N is the number of nucleus for unit volume and a and a are the total
crosssections for K and K . In terms of the forward scattering amplitudes
/ and /, from the optical theorem, a = (4n/k) Im (/) and a = (47i/k)Im(f).
If the forward amplitude is not purely imaginary, the beam is not only atte
nuated but also refracted, then instead of /Im(/) and ilm(f) we should
write simply / and /. Then
 JO > /0  1& W>  2 ^fY t l*> + B \v) >
\K> > JO  iBt {mx>  ^fY t \K> + A \ K >} •
Taking p times the first equation ± q times the second we obtain
\Ly^\L>m{M' L \Ly~(ff)Nr s A s \s>},
\S»^\S>i*t{Ml\S?>%(ff)Nr a A B \L>Y
where
M' L =M L y(f+f)Nr s A s ,
M' s =M' s ^{f+f)Nr s A s ,
and $zf$t = r s A s = k/mjt, where r s is the K s decay length.
Therefore, if f¥=f, \L} and \S) do not propagate independently but they
are coupled. To the first order in a finite slab of material after a time r,
The K L — K s mass difference 261
the state becomes:
L> ^exp [iM' L x\\V>~ J^I M Nr s A s (pxp [/M^Jexp [iM' L r])\Sy .
Thus there is a coherent regeneration of the state »S>. The state at the
exit of the plate is of the general form:
\L> + q\S>,
where q, the regeneration amplitude, is proportional to
% M f L Z f M s Nr sMl™P [(M s M L )r]) .
3.  Single regenerator experiments. The K^K^ interference in the n + n~
decay channel.
It was realized promptly after the discovery of CP violation that the exi
stence of both K L >^ + 7r _ and K s ^tz + tz decays provides a very powerful
method for investigating the K^— K s mass difference. Let us consider the
forward going beam after a slab of material. As we have just seen the state
after the proper time interval t, measured from the exit face of the regen
erator is:
out, O = exp [— iM L t]\L} + q exp [— iM s t]\S) .
Since both L> and \S} states decay into the state ti+tt with amplitudes
<7r+7r _ TL> and <7r+7r7"5'>, the decay amplitude for the state out, t} is:
<jr f jrrout, t} = exp [— iM L t](ji+n\T\V) + q exp ]— iM s tK7i+7i\T\S}
and the decay rate per unit of time is promptly obtained by squaring the
above expression:
dN
w (0 = r(K s >7T+o{^ex P [r s t] + 1*? + _2 exp [r L t] +
+ 2\rj + _ Q \ exp [ (r s + r L ) t/2] cos [8m t Arg(^) + Arg(»? + _)]} ,
where r(K s > tz+tz) is the decay rate of the shortlived state into tz+tz and
V+ = <ji + n\T\L)l<ji + n\T\S'}. The time dependence of the tz+tt decay rate
in addition to the two terms due to Kg and K L decaying into tz + tz~ has an
interference term showing the characteristic precession between the Kjr, and K s
262
C. Rubbia
states due to the mass difference. This interference term can be observed
over a relatively long time interval. In the case of a thick regenerator
g> \v+\ an d f° r ear ly times the term in h+_ 2 can be neglected and to
an excellent approximation also r s \ T L ~r s :
dN
dt
(t)~r(K s ^+izy\ Q \* e xp[r s t) 1
2\rj._
V\ Q \*exp[r s t]
cos ($mt\oc)
The statistical accuracy to which the decay rate can be determined at each t
is also proportional to 1/V\q\ 2 exp[—F s t]. Therefore the error with which
the interference term \r)+\ cos(Sm + a) can be determined is the same at all
values of t for which the approximation ?? + _ 2 ~0 is valid. In practice the
time interval over which the interference can be observed is determined by
the largest regeneration amplitude which can be realized, \Q/r) + _\~50 and by
the contributions of systematic errors.
The timedependent interference pattern has been very extensively studied
at CERN for carbon [7] and copper [8, 9] regenerators. A typical inter
/1.0
10 11 12 13 TdO ,0 sec)
Fig. 1.  Timedependent interference between the CP violating amplitude
K x > 71+tt;" and the K s >tc + tc. The oscillation is showing the characteristic
precession between the K L and K g phases due to the mass difference, o, ref. [14];
•, ref. [9].
The K^— Kg mass difference 263
ference term is shown in Fig. 1. The precession between the K L and K s states
due to the mass difference is beautifully demonstrated over a complete oscil
lation. From the frequency of the oscillation observed in the three investi
gations at CERN [7, 8, 9] the mass difference is measured to be :
8m = (0.543 ± 0.016) x 10 10 s" 1 .
4.  Experiments with two regenerators. The «gap» method and the « zero
cross » method.
Another approach to the determination of the K^ — K s mass difference
consists in using two sheets of matter. In the socalled « gap » method [10]
the regenerated iz + k~ intensity after the second one is determined as a function
of their separation. In the « gap » method events are collected from the
same decay volume for different regenerator geometries whereas the K^Kg
interference method is based on the observation of the decay rate from dif
ferent decay regions for a fixed geometry. This technique is less sensitive to
variations of the detection efficiency over the decay volume but it requires
an excellent monitor and substantial corrections due to interferences with
the CP violating decay K^^Tr+Ti  .
The method can be easily understood expressing the tc+ti  decay amplitude
at the proper time t from the exit face of the second regenerator as the sum
of the contributions of the two slabs and of the component arising from
K £ >7r+7T~ decays. Let At be the time interval between the exit faces of
the two slabs of regeneration amplitudes q x and q 2 , respectively. Then:
<7r+7t T 1 1, A?> = [q x exp [— iM s {t + At)] + g 2 exp [— iM s t] • exp [— iM L At]] •
• <ji+n\T\Sy + exp [— iM L (t + At)](n+7i\T\L) =
= exp [iM L Af ]{[& exp [— i(M s — M L )kt] + q 2 ] exp [— iM s t] •
• (7z+7i\T\Sy + exp [— iM L t]<7i+7r\T\U)} .
As At is varied for a constant t, the last two terms combine to give a fixed
vector, whereas the first one decreases in magnitude and precesses around
this fixed direction. The two pion decay rate can be easily calculated taking
the square of the expression above:
/(/, A0 = I x {t + A0 + I 2 {t) + iVljUt + A0/ 2 (0 cos (Sm A0 / ,
where :
7 = r(K fl ^7c+7r)i ?+ _* f
264
C. Rubbia
i
Z
Z)
O
o
O
O
2
z
o
LU
O
DC
LU
Q.
(/)
z
LU
>
11T
": 3
DO
Z
t i r
l i r
MINIMUM X 1 SOLUTION
USING THE EXPERIMENTAL
VALUES OF F 21 .
* 2 = 1.3
(5 = ±.43
ARG if  ARGti = ±40<
21 '+
—S
J I L
J L
4 6 8
GAP (INCHES)
10
12
Fig. 2.  Number of t+tt events as a function of the gap size and the best fit
to these data (from ref. [11]).
The KrK s mass difference
265
7 1 (r + A0 = /XK fi
^ + [ N 2 exp [r s (t + Af)] + h + _ 2 +
+ 2\Qin+\ exp [— r s (/ + AO/2] cos (8m(' + AO + a)] ,
/ 2 (0 = r(K s > TT+Tt) [ &  2 exp [ r s * ] + h + _ 2 +
+ 2 1 £2*7+ I ex P [— r s t/2 cos (Sm t + a)] .
The terms / > 7^ and 7 2 have a very simple physical meaning. They are the
decay rates one would observe for no regenerator, and only regenerators
1 and 2, respectively. Therefore I x and I 2 have a form analogous to the one
of the single regenerator experiments.
Determinations of Sw with the « gap » method have been reported by the
Princeton group [10, 11]. The results are shown in Fig. 2. The two pion
decay rate has been observed as a function of the spacing between two regen
erators of the same material. The ratio q 2 jq x is then known. However the
A/dependence of the term proportional to cos(8raA0 and of J^f + Af)
are not completely separated out in the fit and the result depends somewhat
on the choice of the parameters like ?? + _, r s , Arg(^ + _). The result of the
most recent Princeton experiment [11] is $m/r s = (0.445 ± 0.038).
In order to overcome these difficulties, a slightly different method, called
the « zerocross » method has been used by a CERN group [12]. These
authors have determined experimentally both I(t, A?) and I , ^(f+Ar),/^),
N,r N t N z
2VN, N 2
DISTANCE BETWEEN BLOCKS l=529.9n
Am=(0.538t00093)xl0*'" sec
v£
2VN, N 2
\
\
\
GEOMETRY 2
DISTANCE BETWEEN BLOCKS l=778.8n
Am=(0.5<i6?0.0082)xl0
5.0 xl0 ,u sec
i\
PROPER TIME
V
\ T
V
Fig. 3.  « Zerocrossing » point of the interference between two slabs in the
experiment of ref. [12]. The two curves correspond to different spacings be
tween the two blocks, a) Geometry 1 : distance between blocks is 529.9 mm.
b) Geometry 2: distance between blocks is 777.8 mm.
266 C. Rubbia
owing to their very simple physical meanings. Then the precession due to
the presence of A? can be evidenced directly from the experimentally observed
rates, as follows:
2V/ 1 (f + A0/ a (0
In order to reduce the possibility of errors coming from incorrect monitoring,
rather than varing the spacing A/ between the two slabs, different values
of A? have been explored taking events of different kaon momenta p K , since
At = A/ra K //?K The most sensitive region is around the value for which
cos(SmA?)~0. For this reason the method is denominated « zerocross ».
Preliminary results from the CERN group [12] are shown in Fig. 3. The
result is
Sm = (0.542 ± 0.0060) x 10 10 s~\
5.  Concluding remarks.
The recent experiments clearly demonstrate the effects of a very small
but finite mass difference between the K L and K s states; when completed
by the investigations of Piccioni and collaborators which have beautifully
demonstrated that the the longlived state is heavier [13] they give a precise
determination of the mass difference.
If the results can be combined with experiments which observe the inter
ference of K L and K s in the 7i + 7i~ decay channel from a state which is pre
ponderantly K (S= + 1) at the production one finds that [14, 15]
Arg(7/ + _) = (41 ± 5)°.
This result is in agreement with a class of theories which give Arg(?? + _) =
= tan 1 (2 8m/r s ) c± 41°, and in particular with the « super weak » for which
such a prediction is exact.
REFERENCES
[1] M. GellMann and A. Pais: Phys. Rev., 97, 1987 (1955).
[2] J. S. Bell and J. Steinberger: Proc. Oxford Conf. on Elementary Particles (1965),
p. 165. In the present paper we shall follow rather closely the formalism developed
in this reference.
The K L — Kg mass difference 267
[3] L. B. Okun' and B. Pontecorvo: Z. Efejp. Teor. Fiz., 32, 1587 (1957). The argu
ment is valid only for Pconserving interactions; see S. L. Glashow: Phys. Rev. Lett.,
6, 196 (1961).
[4] J. Christienson, J. Cronin, V. Fitch and R. Turlay: Phys. Rev. Lett., 13, 138 (1964).
[5] A. Pais and O. Piccioni: Phys. Rev., 100, 1487 (1955).
[6] M. L. Good: Phys. Rev., 106, 591 (1957); 110, 550 (1958).
[7] M. Bott Bodenhausen, X. de Be Brouard, D. Cassel, D. Dekkers, R. Felst,
M. Vivargent, T. Willits and K. Winter: Phys. Lett., 23, 277 (1966).
[8] C. AlffSteinberger, W. Heuer, K. Kleinknecht, C. Rubbia, A. Scribano, J. Stein
berger, M. Tannenbaum and K. Tittel: Phys. Lett., 21, 595 (1966).
[9] P. Darriulat, H. Faissner, H. Foeth, C. Grosso, V. Kaftano, K. Kleinknecht,
C. Rubbia, J. Sandweiss, A. Staude and K. Tittel: to be published in Phys. Lett.
(1969).
[10] J. Christienson, J. Cronin, V. Fitch and R. Turlay: Phys. Rev., 140, B 74 (1965).
[11] R. K. Carnegie: Technical Report No. 44, Oct. 7, 1967, University of Princeton,
Princeton, N. J.
[12] H. Foeth, M. Holder, E. Radermacher and A. Staude; P. Darriulat, J. Deutsch,
M. Cullen, K. Kleinknecht, C. Rubbia and K. Tittel; C. Grosso and M. Scire:
to be published in Phys. Lett. (1969).
[13] R. Good, W. Melhop, O. Piccioni, R. Swanson, S. Murty, T. Burnett and C. Hol
land: Phys. Rev. Lett.
[14] A. Bohem, P. Darriulat, C. Grosso, V. Kaftanov, K. Kleinknecht, H. Lynch,
C. Rubbia, H. Ticho and K. Tittel: Nucl. Phys., B 9, 606 (1969).
[15] D. A. Jensen, S. H. Aronson, R. D. Ehrlich, D. Fridberger, C. NissimSabbat,
V. Telegdi, H. Goldberg and J. Salomon: Phys. Rev. Lett., 23, 615 (1969).
Suggestion for a More Precise Measurement
of the t)+ Phase.
J. Steinberger
CERN  Geneva
Columbia University  New York
This volume represent an effort, on the part of Professor Amaldi's friends
and colleagues, to show some token of their affection and respect. In the
case of this particular contribution, it is unfortunately a very small token.
Quite apart from personal limitations, experimental particle physics moves
slowly and requires the collaboration of many, so that it is rarely possible
to produce a result for an occasion. I am in this way constrained to offer
a mere suggestion for an experiment. It is done with mixed feelings : normally,
I would prefer to wait for the result, but for the occasion I would like to make
some contribution, even if it must be incomplete. I hope that it will be judged
in this way.
It is some years since the discovery of CP violation, but despite substantial
effort, it has been observed only in the K° system. It is possible that we will
continue to be restricted to the K° in the future as well, in our efforts to learn
about CP violation. It is then fortunate that several CP violating para
meters in K° decay, and in particular
n _ <+\r\K£>
V+ ~<+\*\Ks>'
the relative amplitudes of long and shortlived transitions to the charged
pion state, can be measured with precision. In this note I point out a variation
in the present line of these experiments which should permit an improvement
in the measurement of the phase of t] + _ . The same technique is in principle
also applicable to the phase of the corresponding neutral decay amplitude
ratio r] 00 , but the experimental difficulties in7r°7T: decay are somewhat greater,
so that it will be some time before the method can be expected to be useful
also here.
Suggestion for a more precise measurement of the rj + _ phase 269
The ?? + _ phase can be measured by observing the time dependence of the
tc + 7t: decay of a kaon state which is given at time x = 0: *F(0) = q\S} + L>.
This time distribution has the form:
(1) U) = H 2 exp [/>] + *? + _ 2 exp [T L x] +
+ 2^ + _ exp [— Fx ] cos (Am r — q^J .
Here F s and 7^, are the short and longlived widths, respectively; F is
(F s + F L )/2 ; x is the time in the K° rest frame ; and Am = m h — m s .
I + Jx) is plotted in Fig. 1 for a state with q = 1 (V(0) = ^°>). It is
experimentally possible to measure this time distribution accurately, except
in the short time region (shaded in Fig. 1), which is inaccessible for shielding
reasons. Unfortunately, this does not yield a corresponding precision in y n :
Since the <p n dependent interference term is strongest at x = 10 fr s , what
is measured best is the quantity 10 Am/T 5 — 9V* A precise determination
of 9 9 » ?+ _ is only possible if a correspondingly precise value of Am is available.
To be completely explicit, if the error in cp n+ _ is to be less than some number,
say A99, the uncertainty in the mass difference must be less than A(Am/.r s ) ^
A99/IO. The measurement of the mass difference with this precision turns
out to be the bigger experimental problem.
It is the main contribution of this note to point out that the mass dif
ference can be measured with the same apparatus as the 7r+7r~ interference
term, and simultaneously.
The suggestion is to measure, simultaneously with the k+tt decay rate,
also the charge asymmetry in the lepton decay as a function of x. This charge
asymmetry is also governed by an interference between K s and K L am
plitudes; the dominant term has in fact the same form as the interface term
in 271 decay.
If
_ (7c~e + v\r\K} _ AS= A.Q violating amplitude
<7i e + v\x\K} AS— AQ conserving amplitude
and if CPT is assumed, then
(2) (3(7) ^+""^ ^
^ 2(1 — x 2 ) [(exp [— r s r] + exp [— T z t]) Ree + exp [— Fx] cos Amr]
= 1 + x 2 exp[— r s x] + 1— x 2 exp [— T^t] — 4 Im x exp [— Fx] sin Am '
where 7V + and N_ are the decay rates to positive and negative leptons, respec
270
x r s
Fig. 1.  Two pion intensity and leptonic decay asymmetry as a function of
the time in the K° rest frame.
tively, and e is the parameter in the expansion of K L and K s in terms of
K and K:
\S> =
1
[(l+ fi )tf> + (le)*>].
V2(l + e) 2
CPT is assumed, and higher order terms in e have been omitted.
Suggestion for a more precise measurement of the t] + _ phase 271
Expression (2) is also shown in Fig. 1. At long times expression (2)
reduces to the already observed small (~2.7xl0~ 3 ) asymmetry of K. z :
1 — Ixl 2
^T*oo)s S d i = 2Recy r £L
At short times the term exp [ — rr] co s Amr dominates and at time r = 0,
It may be useful here to point out an important feature of this approach.
Both the 2jc distribution (1) and the asymmetry distribution (2) are slightly
modified in an experimental situation, due to several small effects, such as
the propagation of the kaon in the target in which it is produced, and the
scattering of the kaon on the collimators and yray filters which are com
monly introduced. The main effect of this on the measurement of (p n and
Am is to introduce a small phase change <p into both expressions (1) and (2),
so that the arguments of the cosine function in the interference terms are
changed to Amr — (pt, + _\<p and Amr + 99 , respectively. <p , in an experi
ment currently planned, is of the order of (1 =2)°. This is somewhat greater
than the error which is anticipated. However, cp is common to expressions
(1) and (2) and if we think of the charge asymmetry measurement as a deter
mination of the quantity Amr \<p , we can see that in the comparison of
the two distributions cp n can be extracted without separate knowledge of
Am or 9? : This, however, is only a heuristic way of understanding the manner
in which the errors enter. In practice it will be necessary to analyse the two
experiments to find Am and cp . However, the error in AmT+9? for r~lQ/r s
will be smaller than the error in q> Q or in Amr.
It is necessary to discuss here a problem in connection with the measure
ment of the restframe time r in the leptonic decay. Let t = dmjcp, where
d is the (measured) distance before decay, and m and p are kaon mass and
momentum, respectively. The difficulty is that p is not directly measurable
since the neutrino is not observed. It is however possible to proceed as follows.
For each event the directions and momenta of the two charged particles
are measured. We can then define p' = \p + + p~\ (*) and t' = dm/cp', and
tabulate the experimental asymmetry as a function of t'. It is then necessary
to fold the transformation t<>V into the expression (2), a process which
(*) Other definitions of p' , which serve equally well or perhaps even slightly better,
are possible. This definition serves, however, to illustrate the method.
272 J. Steinberger
requires a knowledge of the geometry of the apparatus and the beam mo
mentum distribution. Both of these can be known with sufficient accuracy
so that this step need not necessarily increase the error appreciably.
In the remainder of this paper we will discuss the precision which may
be obtained in y n in a particular experiment. In a proposed experiment, the
kaons are produced at 75 mrad to a 24 GeV/c proton beam. The 'detector
is assumed to have a sensitive decay region between 2.2 and 11.5 m from the
point of kaon production. The main contribution to the result will be from
kaons between 6 and 12 GeV/c, exploring the r interval 4 < r s r < 30. It is
expected that 1.5 xlO 7 leptonic decays and 5xl0 4 K L ^Tz+it decays per
shortlived lifetime can be accumulated in an extended experiment. The
theoretical expressions (1) and (2) are modified to account for the fact that
both K and K are produced at the target. This has the effect of diminishing
the magnitude of the interference term by the factor
/k+V
Experimentally it is known that % varies from 0.5 at 6 GeV/c to 0.85 at 12 GeV/c
for the postulated conditions.
Calculations have been performed which consist of « generating » experi
mental data according to expressions (1) and (2), using the present experi
mental values for Am, r s , rj, cp n , %, etc., and then in turn taking these « data »
and inverting the analysis to find the same parameters. In this latter part
X and <p Q are left as functions of the momentum. The result is that the stati
stical error for cp n is expected to be ~f°.
Of course there may be unanticipated problems in the successful exploitation
of this suggestion, but the experiment is in process of preparation at CERN,
and in a year or two should be completed.
I wish to thank Drs. K. Kleinknecht and P. Steffen for discussions and
the calculations referred to in the last paragraphs of this note.
An Amateur's View (*) of Particle Physics (**).
V. F. Weisskopf
M.I.T.  Cambridge, Mass.
Here are some impressions of a nonexpert on the present state of par
ticle physics.
1.  The third spectroscopy.
One of the most striking aspects in the recent development is the ever
growing list of excited states of the bar yon and meson. Remember the fact
that nine years ago the only states known were p, n, J\P*(1236), 2, A, S,
and 7T, K. Compare this with today's Rosenfeld table. The list is increasing,
more levels are found every year and their quantum numbers become better
known. It is a slow and painful task indeed; each simple level requiring
many manyears of work. It is not made easier by the fact that, often, the
widths of the levels are comparable to the level distances. This brings in a
slightly disturbing feature: Some baryon levels are established only by
phase analysis of meson scattering; they do not appear as a bump over a
background in a scattering experiment. Such things happen very rarely in
atomic or nuclear spectroscopies.
A relatively recent innovation is the production of certain mesons by
electronpositron collisions. This is an unusually clean way of producing a
single vector meson — only that type can be produced singly — free of nearby
sources of strong interaction ; it allows a better determination of the relevant
properties.
(*) Amateur: 1) A person who does something for the pleasure of it rather than
for money. 2) A person who does something more or less unskilfully. (Webster's New
World Dictionary.)
(**) This work has been supported in part by the Atomic Energy Commission under
Contract Number AT (301) 2098. This article is an enlarged version of a similar paper
which appeared in Comments on Nucl. and Particle Physics, III, 1 (1969).
18
274 V. F. Weisskopf
There are a few immediately obvious features in the level structure of
hadrons. In contrast to atomic and nuclear spectra the level distances are
comparable to the mass of the object. A striking feature is the existence of
practically degenerate isotopic multiplets, another is the restriction of strange
ness to negative values S> — 3 for baryons and to S< 1 for mesons; finally
there is a connection between the isotopic spin and the strangeness quantum
numbers. This has led to the classification of levels by SU 3 and the discovery
of SU 3 supermultiplets. The newly discovered levels seem to fit resonably
well into this scheme.
For me, the SU 3 classification is based on the quark model, with three
types of quarks, which hadrons are composed of baryons being three quarks
and mesons being quarkantiquark pairs. Thus, mesons, but not baryons,
can be singly created and destroyed. The trichotomy of quark types is repre
sented by a formalism with three « unitary spins » : isotopic, wspin, and uspin,
each representing the alternatives given by one pair of the three types, just
as the ordinary spin represents the alternative of spinup and spindown.
Isospin and strangeness of hadrons are directly obtained by summing the
corresponding quantities of the quarks; this simple rule explains the actual
relations and restrictions among these quantum numbers. Indeed, one finds
only the angular momentum quantum number to be unrestricted ; a reflection
of internal orbital excitations of the quarks which gives rise to families of
hadrons with equal intrinsic quantum numbers but different angular mo
menta.
If one assumes that the binding force which keeps the quarks together
is independent of the isotopic spin, and weakly dependent on the other spins,
the main features of the baryon and meson spectrum can be reproduced.
The systematics of quantum numbers, the multiplet structure, some features
of transition probabilities between levels, and ratios between decay rates of
mesons fall into place.
Of course, quarks have never been observed. Grave problems arise if
that model is taken too seriously. However, it serves as a simply describable
realization of SU 3 symmetry. The latter is what remains of the quark model,
if one removes the quarks — the grin of the Cheshire cat. Why it works, is
still one of the great miracles.
Whether the quarkidea is correct or not — it is improbable that it will
turn out to be correct in its present simple form — the experimental evidence
of hadron spectra points to an internal structure of the nucleons and mesons.
In some ways the situation is reminiscent of atomic and molecular physics
before Rutherford and Bohr. We know much of the spectrum of the nucleon,
we know something about the force between nucleons; it is a relatively com
plicated force, attractive at larger distances, repulsive at smaller distances,
An amateur's view of particle physics 275
spin and symmetry dependent. In this respect it is similar to the chemical
force between atoms. Only after the atomic structure was elucidated, one
found out that the chemical force is based upon the more fundamental electric
force between atomic constituents. It may well turn out that the nuclear
force also will be understood as a consequence of more fundamental inter
actions and processes within the nucleon.
It would be misleading, however, to overstress the analogy between atomic
structure and nucleon structure. As it was remarked before, the excitation
energies of the nucleon are of the order of its rest mass energy, a circumstance
which introduces new and badly understood features. With the present
mathematical techniques, we are not able to deal with composite systems
where the interaction is so strong that binding energies become comparable
to the rest mass. One of the consequences of this situation is the important
role of virtual particle pairs ; such a system becomes an agglomeration of pairs
of particles and antiparticles ; the number of constituents, as it were, is always
large and indefinite. It is to be hoped that methods can be found to deal
with such conditions.
2.  Electron scattering.
The growing availability of highenergy electron beams is noticeable in
the increasing number of interesting experiments with electrons. The resulting
elastic form factors (electric and magnetic) of the nucleon are not yet under
stood. Their dependence on the momentum transfer q goes as g~ 4 at high
^values. The fact that the form factor decreases smoothly to zero at high
#'s indicates that the nucleon is an extended system and that there is no
hard and small core noticeable at the center of the nucleon. It does not
exclude the possibility that the nucleon is made of hard and small constituents.
It only shows that the charge and magnetic distribution has no accumulation
at the center as it has in the hydrogen atom.
The inelastic electron scattering has turned out to be most interesting.
The excitation of higher baryon states by this process is a repetition of the
FranckHertz experiment, more than 50 years later at a billion times larger
energy scale. The form factor of these excitations seems to have a similar
^dependence as the elastic one — no wonder, since we expect the excited
states to have similar charge and magnetic distributions. An interesting feature
appears when one looks at the very large energy transfers of the scattered
electrons, way above the known resonances. Then the strong ^dependence
disappears and the scattering seems to be independent of the momentum
transfer, apart from the trivial electric charge effects (Mott scattering). A
276 V. F. Weisskopf
lack of ^dependence indicates a scattering object smaller than the length
associated with the momentum transfer. Did we hit here some very small
entity or entities within the nucleon, some constituent or perhaps the quark?
Whatever the detailed interpretation of these results may be, the absence of
a ^dependence at highenergy losses certainly indicates the existence of a
length, small compared to 10~ 14 cm, which should play an important role
within the nucleon.
3.  Current algebra.
How can we look into the dynamic situation inside the hadrons ? Strong
interaction processes seriously distort the hadron under observation. Weak
and electromagnetic processes, however, leave it intact and can be directly
interpreted as the effect of currents inside the hadron. The most obvious
example is the electromagnetic current density j% M (four vector) whose matrix
elements determine, and can be determined by, electromagnetic phenomena.
Similarly there exist four more current densities which, in the same way,
determine the weak interaction phenomena. Why four? Firstly, the weak
interaction as exemplified by leptonpair emission, has two realizations,
nonrelativistically speaking, the spins of the leptons may be parallel or anti
parallel. This is connected with the fact that any weak process is determined
by two currents, /£ and j^ , the vector and the axial current. In addition,
there are two types of weak processes: strangeness conserving and strange
ness changing (JA^J = 0, 1), which leads to two more currents: j%, u j^.
Ideally one could measure all matrix elements of the five current densities,
if every conceivable electromagnetic or weak process were entirely known.
So far, we known very little about them. One most important known fact is
the discovery (GershteinZeldowitch, FeynmanGellMann) that y'^ apart
from a constant, is an isotopic brother of j^ M , that is, it differs only by the
fact that the charge changes in the former. (This difference is a rotation in
the isotopic spin space.) Current algebra is a bold generalization of this
idea, which assumes that all five of them are brothers, they are supposed
to belong to a family of sixteen current densities which I will now describe.
Again we make use of the quark model. Whatever the dynamics are, there
are currents running in this model; for example, we can define three cur
rents which describe the flow of each one of the three components of the
isotopic spin. Since there are two more unitary spins, the £/spin and the
Fspin, one would think that there will be nine currents. However, the three
types of spin are not independent — an /flip followed by a U and a Fflip
brings us back to the original state; therefore, there are, in fact eight
An amateur's view of particle physics 277
independent current densities: j%, X = 1, ..., 8. All of them are vector fields.
The electromagnetic current is included and they are all conserved currents.
The second half of the family is obtained by considering something
which — nonrelativistically— corresponds to the spin density (ordinary angu
lar momentum spin) of the quarks. It represents an axial vector field within
the hadron. If we associate the angular momentum spin density of the
quark (in this nonrelativistic approximation) with its unitary spin com
ponents (/, U, Fspin), we obtain eight axial current densities jf, X = 1, ..., 8.
They are not conserved currents since a « spin density » is not a conserved
vector field.
The weak currents are supposed to be some linear combinations of the
sixteen currents, namely the ones that give rise to the relevant charge and
strangeness change.
What follows from this assumption? Evidently the FeynmanGellMann
relations between the electric current and the vector part of the weak current
is part of this assumption. But there are more; there exist simple relations
between those sixteen currents since, in terms of the quark model, they can
be represented by simple operators. For example, equaltime commutation
relations exist, such as
where f XvK are constants and the zero index refers to the time components of
the current densities. This is equivalent to a sum rule
2(a\M\b)(b\N\a)2(a\N\b)(b\M\a) = const (aPa) ,
b b
where M, N, P, are operators connected with the currents and a and b are
quantum states. One example [1] refers to neutrino crosssections:
lim
da(v P ) ^v)l = 5! (c08 . (?c+28in . (?Q)f
dk 2 dk*
where a{vp) is the total neutrino crosssection of a proton, k is the momentum
transfer, G the weak coupling constant, and 6c, the Cabibbo angle. We are
far from able to test such relations.
Current algebra proper establishes connections between currents, but says
nothing about the currents themselves. There are approximate ways to get
some limited information about the current distribution within the hadrons.
A baryon, for example, can be considered as surrounded by virtual meson
fields. The mesons with lower mass contribute more strongly and at larger
278 V. F. Weisskopf
distances compared to those with higher mass. Thus particularly the pions,
but also the kaons and vector mesons such as the p or w will play a major
role in the « meson cloud ». Therefore, it is plausible that the vector and
axial vector current densities have some relations to those meson fields
which have similar geometrical properties. For example, the vector current
densities, such as the electromagnetic one, should be related to the p, co,
cp fields ; a suitable axial vector current density (the one that carries isotopic
spin) should be related to the pion field, since the divergence of the axial
current density is a pseudoscalar field, like the pion field. Such assumptions
are known under the name of « vector meson dominance » and « pion domi
nance ». The former is equivalent to an assumption that for small momentum
transfers— only for those will this restriction to the lowest mesons hold — a
light quantum interacts with a baryon in a similar way as a vector meson
would, apart from a proportionality constant. That constant is determined
by the electromagnetic properties of the vector mesons, and can be deduced
from the decay probabilities of these mesons into electron pairs. This assump
tion has proved to be quite useful for the prediction of photoprocesses
with baryons.
The relation between the axial current density and the pion field has
many interesting consequences. It is assumed that the divergence of the axial
current density is proportional to the pion field. The proportionality constant
is given directly by the pion decay into a lepton pair and it represents in
some way, the « axial charge » of the pion. This assumption (together with
some assumptions about a reasonable behavior of the matrix elements of
the pion field) gives rise to a connection between the « axial charge » (the
pionnucleon coupling constant), and the axial weak interaction coupling
constant of the nucleon (GoldbergerTreiman relation). The connection
comes about in the following way: The weak interaction of the nucleon is
caused by the axial current, which is proportional to the pion field which,
in turn, is coupled to the nucleon and therefore dependent on the pion
nucleon coupling constant.
The AdlerWeisberger relation is another example which can be derived
from this connection between axial weak interaction and pionnucleon coupling.
Here one also uses current algebra which establishes a connection between
axial currents and vector currents. One then gets an expression for the
ratio of the axial — to the vector coupling of weak interactions, in terms of
mesonnucleon crosssections.
The relation between the axial current and the pion density has an inter
esting bearing on the question of the conservation of the axial current. The
divergence of the axial current density — which should vanish if the current
were conserved — was assumed to be proportional to the pion field. The
An amateur 's view of particle physics 279
pion field in the vicinity of a hadron is spread out over relatively large dis
tances of the order of m" 1 . If this spread is reasonably smooth, one would
conclude that the Fourier components for wave numbers much higher than
m n should be small. Hence, matrix elements of the divergence of the axial
current density will be very small for momentum transfers larger than m n .
This means that the axial current is conserved in this limit. The Partial Con
servation of Axial Currents (PCAC) gives rise to a number of simple relations
for the interaction of soft mesons with hadrons. In electrodynamics where
the coupling is also mediated by a conserved current, absorption, emission
and scattering of long wave length light quanta is given by simple expressions
proportional to a power of the electric charge. We find similar approximate
expressions involving the axial charge for the corresponding pion processes.
4.  Strong interaction processes.
The theoretical description of the interaction between hadrons is a more
complex problem than that of the interaction of leptons or the electromagnetic
field with a hadron. The concept of current densities is adapted to the case
where the interaction is weak and the interacting field is not much distorted
near the hadron. This is the case when one can use perturbation theory
and the first approximation of an interaction is the dominant one. Then the
interacting field is coupled to those features of the hadron which exhibit
the symmetries of the unperturbed field. When hadrons interact among
each other, this approximation method is no longer applicable since the inter
actions are strong. Yet it remains to be seen whether the current concept
can be sufficiently generalized and adapted to problems of strong inter
actions. Perhaps attempts at using a socalled phenomenological Hamilto
nian are efforts in that direction.
Most of the work in hadron interactions is based on a different approach.
The scattering amplitude A of one hadron scattered by another is a function
of the relative energy and the momentum transfer. Since there is no theory
for the calculation of this magnitude, one establishes some general rules to
which the amplitude A is subjected, and then one tries to extract some
theoretical predictions which may follow. The general rules are based on the
following four items:
a) relativistic invariance;
b) causality;
c) unitarity;
d) analyticity.
280 V. F. Weisskopf
Relativistic quantum mechanics tells us how to describe unambiguously
a group of noninteracting particles with definite masses and spins. Every
scattering process begins and ends with such a group. It, therefore, defines
the variables on which the scattering amplitude depends. Items b) and c)
establish relations which the scattering amplitudes must fulfill, such as dis
persion relations and the optical theorem. Item d) contains the assumption
that the scattering amplitude is an analytic function of the relevant variables
apart from certain singularities which have welldefined physical significance.
I suppose that any imaginable and resonable theory will always give rise to
such functions with certain poles, cuts, and definite asymptotic properties.
The importance of item d) comes from two circumstances : First, a pole
of the scattering amplitude represents a stationary or metastable state of the
composite system of the two scatterers ; the relative energy at which the pole
occurs is the mass of the stationary state and the residue is connected with
the coupling constant of the binding force. Some of these poles may have
an overriding influence on the energy dependence of A, which sometimes
may lead to a simple expression for A involving only a few dominant poles.
The second point is the crossing relations: There is a relation between the
amplitudes of two reactions which differ by replacing a particle coming in
by its antiparticle going out, and also replacing an outgoing particle by its
antiparticle coming in. The amplitude of one reaction is an analytical con
tinuation of the other in certain variables. If we know something about
one reaction, we can arrive at some conclusions about the other; for example,
a strong pole in one channel may have a noticeable effects in the other. Here
again the fact that the relevant energies are of the order of the rest masses
of the particles involved plays an important role. Therefore a pole in one
reaction channel may not be so much further away from an interesting energy
region in the crossed reaction, than it is from a relevant energy region in its
own channel. This consideration also shows why crossing relations are rela
tively unimportant in nuclear or atomic physics, where the relevant energies
are small compared to the rest masses.
The most important experimental fact of hadron collisions is the following
one : In the case of elastic scattering and of those inelastic scatterings where
the quantum numbers of the incident and outgoing particles are the same, the
crosssections seem to reach an energy independent asymptotic values at
high energies. For inelastic processes, where quantum numbers are exchanged,
the crosssections vanish as a negative power of the energy. This experimental
result is not yet explained by any theory, but it is often used as a basis of
deriving other results.
A number of conclusions can be derived from this observed asymptotic
behavior, with the help of the items a)d). One is the Pomeranchuk theorem,
An amateur's view of particle physics 281
concerning the quality of particle and antiparticle elastic scattering {e.g.,
7T++P and 7T+P at high energies). Other recent conclusions are the « finite
energy sum rules ». If one assumes — in some cases there are good reasons —
that the difference between the actual and the asymptotic amplitude of a
reaction vanishes stronger than a certain power of the energy (stronger than s _1 ),
the integral of the actual amplitude over the energy from zero up to a finite
energy E is essentially the same as the integral of the asymptotic amplitude
over the same energy range. The upper limit E must be an energy at which
the asymptotic form is already applicable. This relation establishes an inter
esting connection between the low energy behavior governed by resonances,
and the highenergy behavior which sometimes can be predicted by the
Reggepole theory discussed later.
One of the important concepts in describing interactions between
hadrons is the concept of exchange. In every twobody reaction something
is transferred frome one partner to the other: It is momentum only in an
elastic reaction, it can be any intrinsic quantum number in others. (We call
« intrinsic » any quantum number except angular momentum.) It is some
times useful to describe the reaction by asserting that a suitable particle is
exchanged, which is coupled by an interaction with both partners and carries
over the quantities. The situation could be described in the following way:
A hadron is considered as a conglomerate of hadron pairs whose quantum
numbers add up to the intrinsic quantum numbers of the hadron under con
sideration — a proton is a conglomerate of n7i + , K + A, etc. When hadrons
meet they may exchange a member of those pairs. The rules of these exchanges
are hard to get at, since particles in the conglomerate do not behave like free
particles. One must find means how to deal with this situation. The Regge
pole method is such an attempt: One makes use of the crossing relations
and starts from another reaction channel (^channel) in which the exchanged
particle appears under more « natural » conditions, that is as a free particle.
It is the channel where it is created by the fusion of two hadrons (more exactly,
by the fusion of one of the incoming hadrons and the antiparticle of an
outgoing one). In this channel the exchanged particle appears as a composite
system made up by the two hadrons. Such a system may assume a number
of states of different angular momentum each of which may be identified
with some observed particle (Regge families). Each member of this family
has the same intrinsic quantum numbers and could serve as an exchange
particle in the reaction. In terms of a continuous /variable, a Regge family
is represented as a function m(J), where the actual particle masses are the
values of m at integer (or half integer) /'s (Regge trajectory).
The existence of these families or trajectories is exploited to express the
scattering amplitude in terms of a sum of contributions from special poles
282 V. F. Weisskopf
(Regge poles) which appear if the angular momentum is used as a continuous
variable /. Each Regge pole represents not only a single state of the com
posite system, but it encompasses the effects of a whole Regge family upon
the scattering amplitude. It is assumed that these Reggepole contributions
have an overriding influence so that they dominate the scattering amplitude
not only in the ^channel, but also in the actual scattering channel. This may
be an appropriate way of dealing with the concept of exchange in strong inter
actions, which takes into account not only the effect of exchange of one
particle, but of each member of a Regge family. Its main results are state
ments about the scattering amplitude in the limit of small momentum transfer
and highenergy. Hence, it is relevant for the asymptotic energy behaviour
discussed before.
It must be said that these Regge extrapolations from one channel to
another introduce a number of arbitrary functions into the picture such as
the « coupling strength » of the Regge trajectories (residues of the Regge
poles). In order to satisfy the analyticity of A, these arbitrary functions
must fulfill a lot of complicated conditions (evasions and conspiracies), and
new « daughter » trajectories must be introduced which may not necessarily
give rise to observed particles. In view of all these complications, together
with the introduction of Reggecuts — the same kind of treatment for the
exchange of pairs of particles — one may ask whether the Reggepole method
provides deeper insight into what is really going on. I quote Van Hove [2]
« The Reggepole model is not a theory with a high predictive power, but a
refined framework to correlate collisions — especially of inelastic type — to
exchange processes ».
Recently Veneziano has proposed an expression for the scattering am
plitude for the case of mesonmeson scattering which, perhaps, goes a little
further than the Reggepole model. It is a simple expression representing a
specific case of a Reggepole model, in which all Regge trajectories and the
functions describing their coupling strength are well defined. The trajectories
are straight lines (m 2 is a linear function of /) and the fact that only mesons
are involved, introduces symmetries which define all the coupling strength
functions in an unambiguous way. The simplicity and the internal consist
ency of this expression are impressive. It seems that some of the conclu
sions one can draw from this expression are in approximate agreement with
the present experimental knowledge on mesonmeson scattering. Obviously,
the Veneziano expression can only be a first approximation to reality; there
are theoretical and experimental reasons for this. The lack of unitarity is
of the former kind, the approximate nature of the results is of the latter.
It is important to keep in mind that the Veneziano expression is not a theory
of meson interaction. It is a guess at a result, in the form of a simple math
An amateur's view of particle physics 283
ematical example for a scattering amplitude which fulfils most of the con
ditions that are imposed. At worst, it is a simple mathematical example of
a scattering amplitude fulfilling most fundamental requirements; at best,
it may be a first approximation to reality and may have the value which the
Balmer formula had in the development of our knowledge of the hydrogen
atom.
5.  CPvioIation.
After the discovery of parity violation in 1957, Pauli exclaimed in a famous
letter: « God is lefthanded ». Actually, it turned out soon, that this is
not so. God is righthanded in the antiworld where parity is violated in
the opposite sense. However, seven years later we had reasons to feel uneasy ;
Christenson and Cronin, Fitch, and Turlay found out that world and anti
world are not equivalent even if left is replaced by right. In other words,
nature is not CP invariant. (C transforms world in antiworld, P left into
right.)
In order to find extremely small differences between a particle and its anti
particle, one must set up beat frequencies. That means, one must be able
to create a linear combination of the two with welldefined phases. This
can only, be done if there is an interaction which can transform one into
the other. No baryonantibaryon pair would do, since all interactions con
serve baryon numbers. No charged meson pair would do because all inter
actions conserve charge. An uncharged meson with strangeness zero is its
own antiparticle so that it cannot be a candidate for particleantiparticle
mixing. All that is left are uncharged mesons with a strangeness different
from zero. Weak interactions can transform one into the other since they
do not conserve strangeness. Hence, the (K , K ) pair rose to such great
fame.
Thus K and K are related by the transformation CP: CP K = ~ K . As
long as the weak interaction which transforms K into K is CPinvariant,
the two states are equivalent and two linear combinations with slightly dif
ferent energy are formed, a symmetric and an antisymmetric one:
^i — ^o — ^o » K 2 = K \ K .
Since the mixing of K and K is done by a secondorder weak process the
splitting is extremely small; it is of the order of 10~ 5 eV. It is instructive
to think of the analogous situation with two identical coupled pendulae.
284 V. F. Weisskopf
(This analogy was used by F. Crawford in a colloquium talk.) Such coupling
also produces a symmetric and an antisymmetric proper vibration with
slightly different frequencies. Usually the antisymmetric one has more friction
than the symmetric one so that, after some time, the latter one only survives.
The same is true in the (K , K ) system. Friction corresponds to weak decays.
We direct our attention mainly to decay into pions, either into two, or into
three pions, of the total charge zero. Two pions are even under CPtrans
formation, three pions are predominately odd if they emerge from a small
source. Hence, the symmetric combination K 2 (which is odd under CP)
can only decay into three pions, the antisymmetric K ± decays mostly into
two. Since two pions have more phase space, the K x mode has more « friction »
and the K 2 mode survives longer.
If the weak interactions were not CPinvariant, K and K would no
longer be equivalent in this interaction. This would have two consequences :
a) the eigenstates, which we call K s and K L (shortlived and longlived),
would no longer be either symmetric or antisymmetric. They would be some
other linear combination: K s =£ K x , K L ^K % . The same would happen in
the case of two coupled pendulae, if the two pendulae were not exactly equal.
b) The number of decay pions would no longer be an indication of the sym
metry of the decaying state; K 2 would also be allowed to emit two pions.
As the result of both consequences, one would observe that the longlived
eigenstate sometimes emits two pions and not always three. This is what
Christenson et ah, have found to our surprise and bewilderment, and they
have shown that K and K are not equivalent ; world and antiworld are dis
tinguishable. This simplest situation is realized if only consequence a) of
CPviolation occurs. This would be the case with a socalled « superweak »
interaction, which violates CP but is very much weaker than the ordinary
weak interaction. Hence, it would practically not influence the ordinary
weak decay into two or three pions, so that this alternative can still be used
as a distinction between symmetry and antisymmetry. But, because of the
extremely small split between the two modes — secondorder weak inter
action — a very small CPviolating term (of the size of the secondorder of
weak interaction), would destroy the pure symmetry or antisymmetry of the
modes. The longlived mode would not be purely symmetric but would have
a small antisymmetric admixture, which shows up in the form of a two pion
decay. There is an indication that consequence b) may in fact not be present :
The (7c+TT"/7c 7t )ratio seems to be the same in the shortlived and in the long
lived, twopion decay. This fact does not exclude consequence b) but if it
were not so, one would be sure that b) is present.
There is new independent evidence regarding the two modes of the
(K , K ) system, which came from the comparison of the following two
An amateur's view of particle physics 285
decays of the longlived mode:
K i ^7T++e+v, K i >7i+e++v.
If K L were exactly symmetric in K and K , the two decays would be exactly
equally strong. Actually, a group at Stanford and at Columbia [3] have
found a difference of the order of one percent, a direct manifestation of an
inequality of world and antiworld in the K^mode.
6.  General situation.
It is questionable, whether our present understanding of highenergy
phenomena is commensurate to the intellectual effort directed at their inter
pretation. We are able to describe the phenomena in terms of particle fields,
scattering amplitudes, current densities, etc., by using a language which im
plicitly assume that there exists a valid quantum theory of particles with inter
actions — strong, electromagnetic, and weak — which explains everything in a
consistent way along the accepted principles of quantum field theory. The
experiments do not reveal any inconsistency with these principles. On the
other hand, no such theory has yet been formulated. It is impossible to
decide at this stage, whether this lack of success is caused by the mathematical
difficulties of a field theory with strong interaction, or by the fact that we
have not yet found the conceptual framework necessary to understand the
situation.
The present theoretical activities are attempts to get something from
almost nothing; attempts to conclude as much as possible from a few general
restrictions of the formalism, such as relativity, causality, unitarity, and
analyticity. It is astonishing and exhilarating how much, in fact, one can
conclude from so little input. It is a veritable « bootstrap » operation. But
does it lead to a deeper understanding of what is going on within the hadrons ?
Does it give us any insight into what lies behind that wealth of experimental
material on resonances and reaction rates? It is true that the present for
mulation of weak interaction phenomena is impressive in its eloquent sim
plicity. Ideas such as SU 3 and current algebra were very exciting when they
were introduced ; they supplied an appropriate terminology for the description
of facts, they showed how certain phenomena are connected with others,
but it does not appear that they wave brought us much nearer to an under
standing of the subnuclear world. The existence of three types of seemingly
unconnected interactions is still an unsolved problem, although the close
relation between electromagnetic and weak vector currents may be the first
286 V. F. Weisskopf
hint at some deeper connection. We also have no understanding yet of the
nature of the electric charge with its double manifestation as electron and
muon.
Highenergy physics today is an experimental science. We are exploring
unknown modes of behaviour of matter under completely novel conditions.
The field has all the excitement of new discoveries in a virgin land, full of
hidden treasures, the hopedfor fundamental insights into the structure of
matter. It will take some time before we can produce a rational map of
that new land.
REFERENCES
[1] S. Adler: Phys. Rev., 143, 1144 (1966).
[2] L. Van Hove: CERN publication 6831 (1968).
[3] D. Dorfan, J. Enstrom, D. Raymond, M. Schwartz, S. Wojcicki, D. H. Miller and
M. Paciotti: Phys. Rev. Lett., 19, 987 (1967); S. Bennett, D. Nygren, H. Saal,
J. Steinberger and J. Sunderland: Phys. Rev. Lett., 19, 993 (1967).
Some Questions Concerning Adiabatic Transformations.
G. C. Wick (*)
CERN  Geneva
1.  Introduction.
The old questions connected with the socalled « adiabatic theorem » [1]
still play an important role in many questions of quantum field theory such
as renormalization, definition of the vacuum state, etc. It may therefore
be of some interest to simplify or clarify the proof of certain results, even
though they are generally regarded as well known. We refer in particular
to the following: A very common situation arises when a coupling constant
is switched on exponentially, g{t) = g exp [at] ; the adiabatic limit is then
obtained, of course, for a^0 + . For finite a, the state \p g attained by the
system at, say, the time t = 0, satisfies a wellknown differential equation
with respect to the coupling constant g. This equation was obtained by
GellMann and Low [2] by means of a perturbation expansion in the inter
action representation. We note in Sect. 2 that a much simpler and more
transparent derivation can be given, without resorting to a perturbation
expansion. Our main topic, however, is the limit a > 0. As is well known,
the state vector \p g contains a phase factor exp [— id(g, a)] which becomes
singular in the limit a^O, in the sense that d~l fa. Physically, this infi
nite phase must be the integral over time, from / = — oo to t = 0, of AE(g)fh,
where AE(g) is the level shift produced by the perturbation; when a is finite,
this shift operates effectively for a time of the order of 1/a, hence the above
mentioned result. Formally, the existence of the singularity can be easily
checked [2], if one examines the behaviour, in the limit a > 0, of the suc
cessive terms in the perturbation expansion; one finds that the term of
order g n contains singular terms in a, of order or 1 , a 2 , ..., or 71 . It is intui
tively plausible, but not obvious mathematically that these terms arise from
(*) Permanent address: Columbia University, New York.
288 G. C. Wick
the expansion of the exponential phase factor. If this is true, it becomes
possible to eliminate the singularity at a = by renormalization of ip g , for
example [2], by the definition
(1) Xg = Wgf( ( P> W) »
where (p is the initial value (at t = — oo) of the state vector. Here (..., ...)
indicates as usual the scalar product of two vectors. It is, of course, a fun
damental result that % g should have a finite limit for a = 0, because it is
this limit, which is then shown to be an eigenstate of the perturbed Hamil
tonian, as stated by the adiabatic theorem.
Now GellMann and Low content themselves with asserting that all the
above statements can be verified « up to any desired order in g », i.e., pre
sumably as far as one's patience and willingness to be convinced allow.
The direct calculations actually become quite laborious very soon. The
question, however, is so fundamental and simple that it should be settled
completely for an arbitrary order n. We show in the following that this is
indeed possible by utilizing the differential equations in g satisfied by the
state vectors ip g and % g , equations already given by the abovementioned
authors. The connection between the adiabatic solution and the Rayleigh
Schrodinger perturbation series is thus completely established.
2.  The differential equations.
The problem to be dealt with is the following [2]: The Hamiltonian of
interest is of the form
(2) 3? = ^(s) = =^o + s"i> i
One asks for a solution of the timedependent Schrodinger equation
(3) / gy = {^o + S exp [oct] ^} y ,
namely, the solution which for t > — oo behaves asymptotically according to
(4) y)~<pexp[—ie t],
where q> is a normalized eigenstate of the unperturbed Hamiltonian corre
sponding to a nondegenerate eigenvalue e :
(5) (^ e )<p = 0.
In eq. (3), a is a real constant > 0.
Some questions concerning adiabatic transformations 289
We now denote by xp the value of this solution for / = 0. More ex
plicitly, let ip(t, g, a) be the unique solution of eqs. (3) and (4), then
(6) xp g = yj(0, g, a) .
We derive a differential equation with respect to g, satisfied by ip g , as fol
lows. Consider the function:
(7) xp x {t) = exp [is r]ip(t + r, g, a)
which, apart from a phase factor, is obtained from the solution ip by a time
displacement t. Clearly tp ± satisfies the asymptotic condition (4), and also
the Schrodinger equation (3), for a different value of g: g 1 = gexp[ocr].
Therefore, ip x {t) = ip(t, gexp [ocr], a) or:
(8) y(t + t, g, a) = exp [— ie r] ip(t, g exp [ar], a) .
Differentiating with respect to r and setting r = 0, we can express the time
derivative in eq. (3) in terms of txg(dtp/dg) — ie ip. At t = 0, eq. (3) becomes
(9) iocg^ = {^(g)e }y> g ,
which is GellMann and Low's eq. (A. 5).
This derivation does not depend on a perturbation expansion and it can
be easily generalized. For example, assume
(10) JTfe) = 3f + gMT x + £ 2 ^ 2
(or even a polynomial in g of order n) and then consider the timedependent
Schrodinger equation in which J^(g) is replaced by J4?(gexp[oct]). Then
everything goes through as before, and eq. (9) is obtained. In the following,
however, we shall restrict ourselves to the simple case, eq. (2). The gen
eralization (10) is not without interest, however, since Lagrangians and
Hamiltonians with quadratic terms in the coupling constants are quite
common.
Finally we notice with GellMann and Low the following equations of
which the second one is a differential equation for the renormalized state
vector xg'
9
(11) iccg g {(p, ip g ) = (<p, [ &, (g) — £ ] y> g ) = g(<p, 3^np g ) ,
(12) iccg^ = {^(g)e }x g Xgiocg^ln((p, y> ) .
19
290 G. C. Wick
Both equations, of course, follow from eq. (9). In eq. (12), furthermore,
the last term can be modified as follows
8
(13) iocg g In (<p, y> ) = g(<p, 2P X % g ) ,
so that finally
(14) iocg ^ = {jT(g)  E(g, a)} Xg ,
(1 5) E(g, a) = e + g(q>, Jt x Xg) •
As we shall see, in these two last equations, one can go to the limit a =
without any trouble, and E(g, 0) is then the perturbed eigenvalue [of the
operator Jf(g)].
3.  The adiabatic limit.
It is customary to obtain the perturbation expansion of ip g
(16) V9 = v+ ^^ n ^
l E Q — M + icc(n—l) e —Jf + ioc
from the timedependent equation (2). From this, in principle, one can ob
tain the expansion of % g , eq. (1), but, as we have said, this is rather cum
bersome. Notice, however, that (16) can be obtained directly from eq. (9).
It should be almost equally simple to obtain an expansion for Xg directly
from eqs. (14) and (15). For g = 0, Xa = V>g = <P1 assume therefore
(17) Xg = Zg n <Pn(cc),
where (p = <p. Notice also that, from (1): (99, Xa) = h so that we must nave
(18) (q>,<Pn) = &w>\ (n = 0, 1,2, ...).
Substituting (17) into (15) we obtain
(19) E(g, a) = e + 5 g n e n (cc) ,
where
(20) e»(a) = (<p, =3f i^niCa)) .
Some questions concerning adiabatic transformations 291
In particular, £ x (a) = (<p, Jf^) is the firstorder perturbation of the energy
level, and is independent of a. Next substitute (17) and (19) into (14) and
obtain the recurrence relation
(21) (s — JT + iccn)(p n (cc) = ^ifn^oc) — (99, ^ X (p n  X {(£)) <p — 
nX
~^£nm(oc)(p m (oc) ; (n = 1, 2, ...).
m=l
Thus the nth term in the expansion of % g is at first sight much more com
plicated than the corresponding term in (16). It has, nevertheless, much
simpler properties in the limit a = 0. Notice in fact that the solution of
an equation (e — ^f + iocri)(p n = oj n or 9% = (e — Jf + zan) _1 a> w becomes
singular as a>0 only if (99, a> n ) ^ 0. But the righthand side of (21) may
be rewritten
nl
(21') co n = Aye x y n _ x — ^ e n m(pm ,
where A is a projection operator (projection on the subspace orthogonal
to 99). Together with (18) this implies that oj n is orthogonal to 99, and
9% = lim (p n (oc) exists, and may be obtained by solving the recurrence equations
ral
(22) (fi — J5f 0)9% = A^ x (p n _ x — 2 £nm<Pm ,
m=l
(23) e n = (rp, ^ x y n _ x ) .
These are, however, precisely the equations of the RayleighSchrodinger
expansion of the perturbed wave function and perturbed eigenvalue s J r AE(g).
The cancellation of the singular phase factor is therefore demonstrated to
arbitrary order.
4.  Remarks and extensions.
It is clearly possible to extend the above calculations in various direc
tions. For example the conclusions of the last Section could be easily extended
to the case of eq. (10). Also, one could expand 9%(a) and e w (a) in powers
of a and examine nonadiabatic effects; for example, terms up to order oc
in e w (a) are easily connected to the normalization factor in the denominator
in eq. (1), since one can prove, by means of eq. (13), that
9
(24) Info y>„) = ' U E (g')^—if ^ #>+... ,
a J g n=l n
292 G. C. Wick
where
e£> = (de w /da) a „ •
We want to deal briefly with a different extension. The methods of perturba
tion theory, adiabatic switching on, and renormalization, have been applied
not only to the Schrodinger equation but also directly to the field equations
in the Heisenberg representation, as, for example, in the work of Kallen [3]
and of Yang and Feldman [4]. The most important difference from the
previous case is that the equations are nonlinear. Nevertheless a method
similar to that of Sect. 2 leads to some interesting equations. Consider as
an example the scalar field equation
(25) (□ + m 2 )<p(x) = — X exp [xt]qP(x) .
Here x = (x, t) and the coupling constant X is « switched on » by the ex
ponential factor. One seeks a solution which satisfies the boundary condition
(26) <p(x)~ (p (x) when t^ — oo,
where cp is a solution of the homogeneous equation (□ + m 2 )cp = 0. For
simplicity, we limit ourselves to the nonquantized version of the theory [5].
We notice that instead of the boundary condition (26) we may consider
more generally
(26') (p(x) ~ <p (x + £) when * » — oo,
where I = (0, t) is a displacement in "the time direction. In fact <p (x + I)
is also a solution of the homogeneous equation (and in the quantized case,
it satisfies the same commutation law as <p (x)). Now if we call @(x; X, £)
the solution of (25) and (26'), it is easy to prove by reasoning as before,
that satisfies the functional equation:
(27) &{x ;X,£) = 0(x+£;X exp [ or], 0) ,
in other words depends on the three variables t, X and r only as a function
of two variables: t+r and Aexp[— at]. Hence 0(x; X, ) satisfies iden
tically the differential equation
By differentiation one derives from this
(29) ^F = 8^ + 2fla 8A8i + aA 8F + aA 8l'
Some questions concerning adiabatic transformations 293
We now write the differential equation (25) at time t = 0, replacing the
second derivative with respect to time by means of (29). The boundary
condition (26) is replaced by
(30) = <p (x, t) when A = .
The equation obtained may play a similar role as eq. (9). The solution can
be expanded in powers of X, and the coefficients of X n (n = 1, 2, ...) obey
a set of recurrent equations. We do not wish to deal with this any further
here, but we shall content ourselves with the remark that the method seems
to be of some interest also in the more complicated case of the quantized
theory.
REFERENCES
[1] M. Born: Zeits. f. Phys., 40, 167 (1926); M. Born and V. Fock: Zeits. f. Phys., 51
165 (1928).
[2] M. GellMann and F. Low: Phys. Rev., 84, 350 (1951).
[3] G. Kallen: Helv. Phys. Acta, 22, 637 (1949); Ark. Fys., 2, 187 (1950); 2, 371 (1951).
[4] C. N. Yang and D. Feldman: Phys. Rev., 79, 972 (1950).
[5] The complications of the quantized case are discussed by: W. Zimmermann: Commun.
Math. Phys., 6, 161 (1967); 10, 325 (1968).
Range and Straggling of Muons.
R. R. Wilson
National Accelerator Laboratory  Batavia, III.
The range of muons is calculated including radiation, pair production,
and nuclear effects. It is shown that the large individual energy losses char
acteristic of these processes reduce the average range by a factor of In 2
from that which one would get on the basis of simply integrating the aver
age energy loss. The fractional straggling first increases as radiation and
pair production effects become important and then decreases as the energy
is further increased.
1.  Introduction.
The study of the passage of fastmoving particles through matter has
been important since the early days of nuclear physics [1]. Many of the
experimental techniques of detection and measurement of particles depend
on such specific properties of penetration as the total range or as the specific
energy loss. Protons and pions at energies below a few hundred million
electron volts have a welldefined average range, but the effects of nuclear
collisions obscure this definite range at higher energies: The track of the
incident proton becomes completely lost in the accompanying nuclear shower
of secondary particles at energies higher than a billion electron volts. Indi
vidual electrons never show a welldefined range: At low energy, multiple
scattering causes them to diffuse through matter; and at high energies a
shower conceals the initial electron.
Muons are more satisfactory particles to consider from this point of
view because at low energies multiple scattering is not too serious, and at
high energies the effect of nuclear collisions is small. On the other hand,
at high energies, bremsstrahlung and direct pair production do occur to in
crease the energy loss above that due to ionization. The nature of the large
Range and straggling of muons 295
individual energy losses due to radiation markedly increase the fluctuations
of individual track lengths.
The present study is concerned with a quantitative evaluation of the range
and straggling of muons at very high energies. Briefly stated, the range is
smaller by a factor In 2 from what one would calculate by neglecting fluc
tuations; on the other hand, the fluctuations on the ranges of individual
tracks are smaller than might be expected intuitively.
2.  Range calculations.
First let us calculate the range assuming only bremsstrahlung losses be
cause this can be done more or less rigorously, then we will include pair
production, nuclear absorption, and ionization. The calculation will parallel
that made by the author for electrons [2]. Bethe and Heitler [3] give the
energy loss of a particle that has traversed a thickness of matter t. They
approximate the radiation spectrum by
(1) a{k)dk = dkdt
E\n[EI(E—k)Y
where a(k)dk is the probability of the muon energy E radiating a photon
of energy k in passing through a distance dt measured in units of shower
length, i.e., for this application in muon radiation lengths divided by In 2.
Then they find that the probability of the particle of initial energy E having
an energy E after traversing a finite distance t is
(2) w(y,t) = (tl,y)\/(tl)\
in terms of the incomplete gammafunction (t— 1, y)l, where y = \n(EJE).
From this one can find [4] the result we seek, namely
(3) w(y, t)dt = e~ y ydt/t\ .
For large values of y and t, the above equation can be approximated by
the Gaussian form
(4) w(y, t)dt = (2jiy)l exp [ (t  yf/2y) dt .
From this we see directly that the mean range r is
(5) r = y max ,
296 R. R. Wilson
where y max is the value of y at the peak of the Gaussian, and that the root
meansquare straggling of the range s is given by
(6) s = jLx = r* •
21. Ionization loss.  If only radiation contributed to the energy loss,
the range and the straggling would be infinite, however, as the energy de
grades, ionization losses become important and allow us to evaluate y max 
Expressing eq. (5) in terms of energy and then differentiating the mean range
with respect to the initial energy gives the average radiation loss on travelling
a distance dt,
< 7 > £*■
That this is neither obvious nor trivial is clear if we remember that we are
using shower units of length which introduce the factor In 2.
Now let us express the energy in units equal to In 2 times the critical
energy /S, i.e., the energy lost by a muon to ionization in going a distance
of one muon radiation length. Here we are making the rough approxima
tion that the ionization loss is independent of energy: we will examine the
validity of this later. We add the ionization loss to (7) to get
(8) — dE/dt = E+l
and integrating this over the energy gives the mean range,
(9) r = log (£ + l)>
which in units of radiation lengths becomes
(10) r = ln21n[(£o//81n2) + l].
Now let us turn to straggling which is manifest in the distribution de
scribed by eq. (3). Equation (6) shows us rather surprisingly that on the
basis of radiation loss alone the fractional straggling sir varies as 1/r*, i.e.,
becomes smaller as the energy increases. Actually the straggling at low
energies will be less than given by (6) because the energy loss due to ioniza
tion has been neglected. The energy loss due to ionization for a muon trav
eling a distance r is just equal to r in the peculiar energy units of the above
theory, hence a fraction of the range r/E can be ascribed to ionization loss.
The straggling of this fraction will be less than 1 % ; hence for any energy
Range and straggling of muons
297
for which this calculation can apply, we can neglect it completely. The re
maining fraction of energy that is lost to radiation processes (1 — r/E ) will
vary roughly as given by eq. (4), which will only be valid when the fraction
(l — r/E ) is large. As a rough interpolation formula, suggested by Monte
Carlo calculations [2], we can write
('if
and remember that the Gaussian distribution has a cutoff at a range equal
to E in shower units or E/fi in radiation lengths.
2'2.  Pair production and other energy losses.  Up until now we have
neglected direct pair production as well as nuclear interactions. In fact,
the loss of energy due to the direct production of electron pairs is compa
10'
1 1 — I I I 1 1
I I I 1 1
1 1 I 1 . 1 I I I.
10
100 10 3
E (GeV)
10<
FIG.1
Fig. 1.  The range and straggling in various materials.
298 R. R. Wilson
rable (within about 10%) to the loss due to bremsstrahlung [5]. The energy
loss due to nuclear interactions amounts at most to a few percent of the
total loss, being relatively larger for light elements and at high energies.
On the basis of a Weissacker Williams consideration of direct pair produc
tion, we can expect the atomic shielding factor to be almost identical to that
for bremsstrahlung. Thus, except for the lowest energy losses where the
mass of the created pair becomes significant, we can expect the two pro
cesses to be roughly the same.
In order to include these effects, I suggest that we define a muon inter
action length in place of the muon radiation length that we have been using
thus far so that the above theory will be valid. Until a more exact calcu
lation of the muon interaction length is made, I suggest that we use simply
one half of the muon radiation length. On this basis, the range and strag
gling in various materials has been computed and is plotted in Fig. 1 . The
range in uranium is significantly smaller than that given in ref. [5] where the
effects of fluctuations were neglected.
REFERENCES
[1] H. Bethe: Ann. Phys., 5, 325 (1930); N. Bohr: Phil. Mag., 25, 10 (1913).
[2] R. R. Wilson: Phys. Rev., 84, 100 (1951).
[3] H. A. Bethe and W. Heitler: Proc. Reg. Soc. {London), 146, 94 (1934).
[4] Using
y
\x l e x dix = t\ — eV^t\lp\yP
o
which can be derived by successive partial integrations (for integral i), one obtains
eq. (3) by taking the difference between t and (r — 1). This procedure was shown to
me by S. Pasternack: originally, I simply guessed the result [3].
[5] R. H. Thomas: UCID 10010, July 2, 1964.
The Basic SU 3 Mixing: co 8 ^ w 1#
A. ZlCHICHI
Istituto di Fisica delUUniversita  Bologna
Istituto Nazionale di Fisica Nucleare  Sezione di Bologna
1.  Introduction.
The purpose of the present paper is to review a basic problem of SU 3
symmetry, the (co(J>) mixing, and to describe the first direct measurement
of the socalled (co<j>) mixing angle.
l'l. The origin.  The (co(j>) mixing has played a basic role in the under
standing of hadron spectroscopy and therefore in the discovery of SU 3 [1, 2].
In fact, without guessing the SU 3 symmetrybreaking it would have been
impossible to establish its existence. The regularity of SU 3 symmetrybreaking
follows the observed regularity of the other symmetry breakings (such as:
isospin by electromagnetic interactions, and C, P by weak interactions),
and represents an aspect of particle physics that is even more spectacular
than the existence of SU 3 .
As is well known, SU 3 symmetry is not an exact symmetry law. When
mediumstrong interactions are switched on (their strength in supposed to
be about onetenth of the strong interaction strength), SU 3 symmetry is
broken. By assuming that the symmetrybreaking term is a coherent super
position of an SU 3 singlet and the eighth component of an SU 3 octet, the
celebrated unitary symmetry mass formula, first derived by GellMann [1]
for a unitary octet and then generalized by Okubo [3] to any unitary multiplet,
is obtained. This GellMannOkubo mass formula (linear for fermions,
quadratic for mesons (*)) was found to be in good agreement with all observed
(*) A simple argument to justify the rule of linear expressions for fermions and of
quadratic expressions for mesons is due to Feynman, and is based on the fact that the
mass term in the Dirac and in the KleinGordon equations is linear and quadratic, re
spectively.
300 A. Zichichi
mass values for the pseudoscalar meson octet, the spin  + baryon octet and
the spin f + baryon decuplet (*). Surprisingly enough, the GellMann
Okubo mass formula failed to explain the observed vector meson masses.
More precisely, the situation concerning the vector meson octet was the
following: from the known mass values of the K* and of the p mesons,
raic* = 888 MeV, m p = 750 MeV. the isoscalar vector meson was expected
to be at m I=0 = 930 MeV. But the comeson mass was known to be at
m u = 780 MeV. It was indeed very disturbing to find that the regularity
of the GellMannOkubo breaking failed so badly to explain the observed
spectrum of the vector mesons. This was the sitation in 1962 when Sakurai [5],
on the basis of the discovery of the 1=0 vector meson at 1020 MeV (the
cj)meson) by the BrookhavenSyracuse Group [6], put forward the proposal
that the cause of the failure of the GellMannOkubo mass formula was the
fact that the co and <j> mesons were two particles with identical quantum
numbers, as far as spin parity, isospin, and (7parity are concerned. The
only difference (if any) between co and <j> would be their SU 3 attribute. But
SU 3 is only an approximate symmetry. Therefore it is reasonable to suppose
that the 780 MeV comeson and the 1020 MeV (j>meson are coherent super
positions of two pure SU 3 states: a pure SU 3 singlet co 1? and the eighth com
ponent of a pure SU 3 octet co 8 . On this basis Sakurai [7] was able to construct
a simple dynamical model of basic SU 3 symmetrybreaking that could account
for the success of the GellMannOkubo mass formula.
It should be clear at this point that it is more appropriate to speak in
terms of (cogcO]) mixing, rather than (co^) mixing (**).
The crucial point was then to check if this mixing really exists in nature.
For a long time the only experimental information on the (cocj>) mixing was
obtained from the observed mass spectrum of the various vector mesons.
But this is more a way of adjusting the GellMannOkubo mass formula,
than a measurement of the (cogco!) mixing.
1*2. Attempts to measure the (cogcoj) mixing.  A way of measuring the
(cogcoj) mixing was suggested by Sakurai [7], who pointed out that if the §
(*) To be more precise, at that time the tenth member of the J p = f + decuplet,
the QT baryon singlet, was still unobserved, but only theoretically postulated [4]. Nev
ertheless, the famous equalspacing rule, i.e., the proportionality of the mass M to the
hypercharge Y, M = M (l + aY), which is a straightforward consequence of the GellMann
Okubo mass formula, was very well satisfied for all the other observed members of the
baryon decuplet JV (1235), Y*(1380), and Ef(1530).
(**) An analogous situation occurs in weak interactions where the (K°K°) mixing pro
duces the physically observed K° and K^ states. Notice that K° and K°, like co 8 and to l5
remain unobserved as particle states.
The basic SU 3 mixing: cogi^to! 301
width TV*!! is calculated from the known p width and compared with the
partial width T^kk, the mixing angle is obtained through the relation
^ = cos* 2 d .
1 <[)>.all
This is because in the decay <]> > KK the coj cannot contribute. In fact to x
can only be coupled to a symmetric bilinear expression involving two pseudo
scalar K's, which consequently cannot be in a state with J =\.
The value of 6 deduced in this way has been controversial because of
the different results obtained for the branching ratios of the cj> decays
(<}> > 3n and (f> > KK) in various laboratories [8] : these results led to values
of d with one standard deviation limits ranging from 0° to 55°. Other ways
of determining 6, as for instance those suggested by Glashow [9], have also
not led to any positive result. The first significant « indirect » value for the
(cogcoi) mixing angle was obtained by Massam and Zichichi [10] via a world
analysis of the nucleon electromagnetic form factors.
1'3. The direct way.  All these suggestions were put forward and the
corresponding attempts were made because the direct clean way of checking
the (cogcoi) mixing hypothesis seemed to be quite remote from the experi
mental area. As we shall see later, this « clean » and « direct » way is either
via the study of the electromagnetic decay modes of the to and (J> mesons, i.e.,
Ico > y > e + e _ ,
9 > y > e + e ,
or via their production through (e + e _ ) colliding beam machines:
(2)
e + e~>y >co
e + e~>Yxj> .
The major difficulty connected with reactions (1) is that the to and §
mesons decay via strong interactions, and their electromagnetic channels
are expected to be depressed by a factor of the order of a 2 (where a is the
fine structure constant): This means that the branching ratios
(3) r " +e_
^covail
and
(4) ^:
302 A. Zichichi
are expected to be of the order of 10 4 . Moreover, there were also difficulties
associated with the production processes of the co and (j>.
The to production could go with a reasonable crosssection via the reaction
(5) 7r+p^co+n,
but, as the wmeson mass is enveloped in the large width of the p mass, a
large background of p's was expected to be present; thus it was necessary
to choose, if possible, those experimental conditions where the p contribution
is depressed in favor of the co production.
The (J) production was observed with a reasonable crosssection in reactions
where strange particles were present, such as K _ p^A°(j), but was expected
to be depressed by a large factor (due to the Aquark spin conservation),
and in fact remained unobserved for a long time, in simple reactions such
as [11]
(6) 7r+p^(j)+n.
Finally, in order to observe w and § decays into (e + e~), it was obviously
necessary to devise a large acceptance experimental apparatus, able to select
and measure angles of emission and energies of the final products of reac
tions (5) and (6), which are neutrons and (e + e~) pairs. The feasibility of
such an experimental program was shown in an unpublished paper by Dal
piaz et al. [12].
The difficulty connected with reactions (2) lay in the fact that (e+e~)
storage rings had to be built. On the other hand, no serious problems of
particle identification or of strong background could be foreseen in the
study of these processes, the feasibility of the experiment being confined to
the problems connected with the construction of moderateenergy (e + e~)
storage rings [13].
As we shall see later, the first measurement of the (cogcoj) mixing was
obtained via the study of reactions (1).
As mentioned before, the (cogo^) mixing was at first described by Saku
rai [5] using a unique mixing angle 6, but by now there are four (cogcoj)
mixing angles quoted in the literature [5,6,8, 1418]; the original 6, then
6 Y and 6 N , and finally the generalized mixing angle d G .
2.  The four mixing angles.
2'1.  Schematic derivation.  We shall now try to review the origin of
all these mixing angles. The starting point is: two particles with identical
quantum numbers (J pa , I, Y) such as co 8 and (Oj will convert into each other
(7) cog^co!,
The basic SU S mixing: (Og^o^ 303
because process (7) does not violate any conservation law but that of SU 3
symmetry, which is broken by the moderately strong interactions. As it is
impossible to switch off these interactions, process (7) will go.
When two particle states can convert into each other, as in process (7),
the inverse propagator that describes the mixed system can be shown to
have the familiar form
(8) D = AK 2 + BM 2 ,
where A and 5 are 2x2 matrices (if we want to describe mixing between
two particles only), K is the quadrimomentum, and M is the mass of the
two states. Let D , A , and B be the quantities defined above before the
mixing starts. Without mixing the two matrices, A Q and B are diagonal, i.e.,
(1 Ov
ft
0>
4> =
■
B =
\o 1/
\o
ft>
and the inverse propagator
(9) D = A K 2 + B M 2
gives the two propagators of the two unmixed states, each having momentum
K and masses ftM 2 and ftM 2 (ft and ft are just numerical coefficients).
The effect of mixing can be of two types. These two ways of treating the
mixing between two particles have been discussed first by Coleman and
Schnitzer [15] (CS) and later by Kroll, Lee and Zumino [16] (KLZ), who
particularly emphasized the need of having two mixing angles.
2' 1.1. Mass mixing. Here it is supposed that the effect of mixing
(process (7)) is that of destroying the diagonality of the matrix B Q , which
becomes B = B + 8B, without disturbing the matrix A .
The problem is to diagonalize B and hence D without destroying the di
agonality of A Q . It is well known that in order to achieve this, the matrix
that is needed can be an orthormal matrix. As the elements of a 2 x 2 matrix
are four, and the orthonormality conditions are three, all the mixing can be
described using a single parameter: the mixing angle 6, which is the angle
first introduced by Sakurai [5]. The left side of Fig. 1 shows a synthesis
of the above chain of arguments.
304
A. Zichichi
(togo^) MIXING
D = AK 2 + BM 2
Without mixing: A =
1
1/'
h
ft
Effect of mixing
i) Massmixing
ii) Current mixing
\
1
Destroy diagonality of
Destroy diagonality of
Bo
A
1
I
Problem: diagonalize
Problem: diagonalize
B = B + 8B
A = A + 8A
Without destroying diagonality of
Without destroying diagonality of
*(i J) *"
compare
*(!' 3
\° V
I
i
Matrix needed:
Matrix needed:
a P\ with orthonormal
y fi] ' ity conditions:
y2 __ ^2 = 1
ay + j5<5 =
4 Parameters  3 Conditions
I
Only one parameter
a
y 8
no orthonormality conditions
4 parameters:
(2 coupling constants: # r ; £y
2 angles: r , 0^
Correlated
I
— tan r = ^ tan 0^ = tan G
Wa m, A
Fig. 1.  (cogQj) mixing: schematic comparison between the « massmixing » type
and the « currentmixing » type models.
The basic SU 3 mixing: cog^o^ 305
21.2. Current mixing. Here it is assumed that the effect of mixing
is to destroy the diagonality of A , leaving B diagonal. The problem is now
to diagonalize A = A + $A, without destroying the diagonality of B .
Notice that B is diagonal but (unlike A ) not unit matrix. In order to diago
nalize A without destroying the diagonality of the nonunit£ , a 2 x2 matrix,
without orthonormality conditions, is required. The mixing must threfore be
described using four parameters, which can be expressed in terms of two coup
ling constants g Y and g N , and of two mixing angles 6 Y and 6 N (here we use
the same notation as KLZ). However, because of T invariance, A and B Q
are symmetric matrices; this gives one condition for the four free parame
ters. This condition can be used in order to establish a relation between the
two mixing angles Y and 6 N , i.e.,
tan 6 Y _ ml
tan N ~ ml '
first derived by KLZ. This relation can be rewritten as
(10) — tan0 F = ^ tanfljy = tan(9 G ,
thus allowing the mixing to be expressed in terms of the « generalized »
mixing angle 6 G [18]. The righthand side of Fig. 1 illustrates the above
chain of arguments.
2*2. Why are there all these complications!  After the introduction of
the (wgcoi) mixing hypothesis by Sakurai [5], CS [15] emphasized that the
Sakuraitype of mixing, called by them « particle mixing » and by KLZ [16]
« massmixing », was not adequate enough to describe mixing between « vector
particles ». This is because vector particles are believed to be associated
with conserved quantities, and « mass mixing » is incompatible with this
requirement, as can be easily shown with the following example. Suppose
that the inverse propagator D describes the isoscalar form factor of the
nucleon (*) and that we choose the « mass mixing » model. After mixing,
D becomes D,
D = A K 2 + B M 2 ^^ D = A K* + (B + Sfi)M 2 .
At K 2 = 0, D ^ D. But the value of D and D at K 2 = is related to
the nuclear isoscalar electric charge (i.e., electric charge of the proton divided
(*) Pole dominance is of course assumed.
20
306 A. Zichichi
by two). The effect of « mass mixing » is to change the value of the nuclear
isoscalar electric charge and this is unacceptable.
If we choose « current mixing » we have
D = A Q K 2 + B M 2 ^ oixias > D = (A + SA)K 2 + B M 2 ,
and at K 2 = it is D = D. This is the reason why « current mixing » is
believed to be more adequate for the description of the mixing between
vector particles.
It is interesting to notice [15] that if the force mixing the particles is truly
weak, « mass mixing » and « current mixing » are indistinguishable (as in
the case of the (K°K°) mixing which produces the physically observed states
K° L and K°; in fact here the transition K°^±K° is a secondorder weak
interaction (*)). Notice that in the above models of mixing it has always
been assumed that the mixing alters only the propagators and not the vertex
functions. Notice also that both « current mixing » and « mass mixing »
are compatible with the transversality conditions for the source of the vector
mesons [16], i.e., the currents to which they are coupled are conserved
currents.
2*3. The crucial point.  The conclusion of all the above arguments is
that the physically observed states <o and <j> are mixtures with certain per
centages (%) of two pure SU 3 states, co 8 and o^:
CO = (%)G>8 +(%)*>!,
<> =(%)** +(%)<■>!•
The problem is how to measure these percentages.
Suppose we have a selective interaction, i.e., an interaction which is
coupled to co 8 and not to o^. If we can find such an interaction, we can then
see how much co 8 there is in the physical states co and ej>.
There is a good candidate for this selective interaction: the electromag
netic interaction. In fact, remember that all known particles obey the
famous GellMannNishijima relation
(11) g = / 3 +  + nothing.
(*) A simple way of seeing why in this case there is no difference between mass mixing
and current mixing is to notice that CPT implies w K » = m s „, and therefore B turns out
to be a diagonal and unit matrix.
The basic SU 3 mixing: cog^coj 307
It could be argued that even if the electric charge Q of all elementary par
ticles has no contribution from quantum numbers which are not I 3 and Y,
the electromagnetic current J^ can still contain a singlet SU 3 term: /^ =
= /£ 8) + J^ I n fact, if the fourth component of Jft has vanishing volume
integral, then:
(12) Q =J4 8 Kx, t)d*x +jji 1 Kx, O&x ,
and the GellMannNishijima relation (11) remains unaltered. Here the
difficulty with the electromagnetic current becomes clear. In fact the octet
part of the electromagnetic current is a Uspin singlet (U transformations
leave the electric charge invariant). All SU 3 predictions based on £/spin con
servation alone cannot distinguish between the octet part and the singlet
part of the electromagnetic current. In order to measure the octet part Jj?>
and the possible existence of a singlet part J™ in the electromagnetic current,
it is necessary to devise an experiment where these two parts can be directly
observed ; the cleanest known example is the measurement of the (e + e~) decay
rates of p, o>, §. In fact, if we believe in the onephoton approximation,
these decays go via the following Feynman diagrams:
The octet part of the electromagnetic current J (8) couples to the isospin (i.e.,
the p meson) and to the hypercharge Y (i.e., the <o 8 part of the co and §
mesons). The singlet part of the electromagnetic current J^ ] couples to the
(Oj part of the co and § mesons. Therefore if we measure the decay rates of p,
oj, and <j> into (e+e~), we do study the coupling of the photon to the isospin, the
hypercharge, and the SU 3 singlet.
308 A. Zichichi
To recapitulate, we have said that we wanted a selective interaction,
coupled only to co 8 , in order to check the (ov^i) mixing hypothesis; but
what we have found is a « good candidate » for the required selective inter
action.
2'4. Conclusion.  The study of co > e + e~ and <J> > e+e~ will allow the
(cogco^ mixing hypothesis (in the limit where the photon is not coupled to Wj)
to be checked; the comparison of the decay widths .Tw^e+e, i^^+e with
.TpHs+e, will allow checking of the consistency of the selectivity hypothesis
we made on the electromagnetic current, i.e., the SU 3 nature of the electro
magnetic current.
3.  Vectormeson photon interaction.
3' 1 . The first derivation.  In order to study the processes
(13)
p ^e+e"
(o > e+e~
i > e + e~
it is necessary to know how to describe the coupling of a vector meson with
the photon ; in fact, as mentioned above, these processes, in the onephoton
approximation, are represented by the following Feynman diagram, where
V stands for the three vector mesons p, co, cj>.
GellMann and Zachariasen [19] were the first to treat the problem of
vectormeson photon interaction and to find out the effective vectormeson
photon coupling constant on the basis of vectormeson dominance. Their
argument is as follows. Consider the 7r electromagnetic form factor (EMFF),
F n (q 2 ). If we assume pmeson dominance, i.e., that the isovector photon is
always coupled to the pmeson, then the pion EMFF will be given by
the following expression:
(14) F n {q 2 ) 
q 2 '
The basic SU Z mixing: cog^coj
309
which can be easily derived by inspecting the corresponding Feynman dia
gram for the elastic (e7t) scattering, where g Pr is the effective (py) coupling
constant and g pmz is the (pn) coupling constants and {m*\q 2 )~ 1 is the p
propagator. At q 2 = 0, the pion EMFF is by definition equal to 1 (in units
of the electron charge):
therefore :
(15)
FJjS)=l
Spy
Spy SpTCTZ
mi
m
gprnz
If we introduce the universality condition for the pmeson hadron coupling,
gffim=f P 'Ig i Spy becomes:
(16)
_m\
Spy f
Jp
where f p is the coupling of the pmeson to the isospin current. In fact uni
versality of the p coupling to the hadrons means that the coupling of the
pmeson with its source density, the isospin current, is universal (at q 2 = 0),
i.e., the ratio of amplitudes for any hadronic state A going into (A+p) and
any hadronic state B going into (B+p) is just proportional to the ratio of the
appropriate /th components of the isospin of A and B:
A^±A+p
B^±B + p
If
I?
3' 2. The question of gauge invar iance and pole dominance.  The simple
relation (16) was obtained by GellMann and Zachariasen [19] by treating
the coupling between the vector mesons V^ and the electromagnetic field A^
in the simple way
(17)
e'VpAp ,
310 A. Zichichi
where « e » is the electromagnetic coupling constant. This interaction pro
duces pole dominance but manifestly violates gauge invariance.
Feldman and Mathews [20] remarked that in order to have a gauge in
variant electromagnetic interaction between the vector mesons and the electro
magnetic field, it is necessary to work with interaction terms of the type
(18) G^F^,
where G^ v is analogous to
F — ^ Av ^ A/x
» v ~~ ax 8x '
for the vector mesons, i.e.
av 1 _dv.
The interaction (18) has the advantage of being obviously gauge invariant.
It is in fact constructed using the fields instead of the potentials, but gives
no pole dominance. In fact (*)
/ 1Q \ r • f _ ** *" • rfi
\ Ly ) "a" r i xv ~~~ Q z i m 2 v '
and this expression vanishes for q 2 = (real photons) (**).
At this point it seemed there was no way out: one either had to
i) choose eV^A^, then get pole dominance but lose gauge invariance;
ii) or choose G^F^, then keep gauge invariance but lose pole domi
nance in the sense that the interaction of vector mesons with real
photons vanishes.
3'3. The KrollLeeZumino theory.  The solution to this trouble was
found by Kroll, Lee, and Zumino [16], who were able to reconcile pole
dominance and gauge invariance in the description of vectormeson photon
interaction. For simplicity we will again consider only the pmeson photon
term. Their argument goes as follows: Add to formula (19) another term
KeJfi,
(*) For simplicity we include only the pmeson photon term. The w and § terms
are analogous but are longer because of their mixing.
(**) The interested reader can find these points discussed further in: The Nature of
the Photon, lectures given by A. Zichichi at the Enrico Fermi International School of
Physics, Varenna, September 1969.
The basic SU 3 mixing: cog^coj 311
where I is a constant to be chosen later. Thus the total interaction
term is
(20) k{b„ • yp) + ^rh <f = ¥rK ^ 2 + m p) + ^ •
J ^ ** q 2 + rm q l + m* H
In the KLZ theory, K turns out to be: K = — \, as a consequence of the
physical requirement that the expression (20) should vanish for # 2 >oo.
The interaction term (20) then becomes:
(21)
?2 _l_ M/.2
+ m i
Pole dominance is reestablished in a gauge invariant theory of vectormeson
photon interaction. It should, in fact, be emphasized that the « pole domi
nance » result (21) is achieved by KLZ not via the introduction of a term
of the form q^A^ in the Lagrangian, but by establishing a special relation
between the « direct » source term Jfi'A^ and the gauge invariant pmeson
photon interaction G^F^. For clarity we draw the Feynman diagrams cor
responding to these terms:
direct photonhadron coupling
(only isovector hadronic current)
gauge invariant
pmeson photon interaction
A JP
G F
[IV flV
An interesting point to remark is that as far as the effective coupling be
tween vector mesons and real photons is concerned, the KLZ result coin
cides with that of GellMann and Zachariasen:
= .K
Spy e i »
Jp
and analogously for co and <}>.
In the language of KLZ, the interaction of the electromagnetic field with
p, co, § takes place through the coupling of the electromagnetic field with the
isospin current J* and the hypercharge current J*, whose explicit expres
312 A. Zichichi
sions are (*)
(22)
I [AqI
(23) J8 = ( cos r . /n 2.^_ sin0r . /M 2. o> ^ j
JY
where q^, eo^, <f> are the p, <o, cj> field operators, and r is the hypercharge
mixing angle already mentioned. Notice that the electromagnetic field couples
only to J% and J^ (the exact validity of this statement has already been dis
cussed in Sect. 2'3), and from formulas (22) and (23) the effective (p, co, (j>)y
coupling constants are derived to be:
(15a)
#PY e ' f '
J P
P
e^sin0i
JY
e7^cos0 ]
JY
The predictions for the (e + e~) decay rates of the vector mesons are, accord
ing to KLZ [16] (and to previous estimate [19, 21, 22]):
(24) T^e = J (jr 2 j m p ,
(25) /^ve+e = °j l^Wsin 2 ^ ,
(26) ^^e+e = j I72) m^ cos 2 B Y ,
(for the notation we follow KLZ).
In these expressions SU 3 symmetry has not been used. If SU 3 is valid,
f Y = \/3f p and 6 Y = 0. If we assume the « naive » SU 3 symmetrybreaking,
then 6 Y = 35° and we obtain the wellknown relation between the partial
decay widths of the various vector mesons:
(27) ^p>e+e .' ^co>e + e ' ^jj^+e = 9 .' 1 ! 2w ,
(*) Notice that J* and /® are th third and eighth components of /^ 8> . However, the
SU 3 relation between / and / will be fixed later.
The basic SU 3 mixing: cog^o),^ 313
where w is an unknown factor resulting from the fact that the mass of the
§ is different from that of the p and co.
3'4. The generalized Weinberg spectral function sum rules.  For the pur
pose of checking the (o) 8 «i) mixing hypothesis, it is sufficient merely to show
that (o » e+e~ and <j> > e+e  both exist (*). Further developments of the
mixing theory can be checked if we compare the partial decay rates (25)
and (26), which give us
tanfl,  V "V r «
'Y
and in terms of the generalized mixing angle 6 (see eq. (10)) :
(28) tan0 o = = — tan d Y .
Vffl^ • /*_*+«, ™*
As mentioned before, in order to have a selfconsistency check on the
SU 3 nature of the photon, it is necessary to compare iV^+e an d JV>e + e
with Tp^+e, using for example the relation (27) (where it should be empha
sized that the factor « w » remains unknown).
A more stringent relation can be established between T p _>e + e> Tows+e
and TV^+e if we believe in the First Generalized Weinberg Spectral Function
Sum Rule (FGWSR). Great interest in the Weinberg Sum Rules [23] was
sparked from
m Ai = V2m p ,
obtained from the first and second WSR, assuming pole dominance and the
KSFR relation [24]. The two Weinberg Sum Rules related objects carrying
the same isospin. The generalization produced sum rules relating objects of
different isospin. According to Das, Mathur, and Okubo [17], and to Oakes
and Sakurai [18] (we shall refer to them as DMS and OS, respectively) the
generalization of the first WSR establishes the following relation among
the (e+e~) vector meson decay rates: (**)
(29) $ m p ■ Tp^+e = ra w • r a ^ +e  + m$ • r^_^ +e  .
(*) Assuming the selectivity of the electromagnetic interaction (see Sect. 2" 3 and 2'4)
(**) This relation can easily be derived using eqs. (31), (15a), (24), (25) and (26), and
remembering that the isovector coupling of the photons is y/3 times stronger than the
isoscalar coupling.
314 A. Zichichi
Furthermore, the « current mixing » result [16] between the two mixing
angles B Y and 6 N (see relation (10)) is also derived from the 1st GWSR [17, 18]
(30) tan0 G = ^ m « r <*^ = ^ tan0F = ^ tan ^
This seemed to imply [18] that in the vectormeson dominance approximation,
the « current mixing » model of KLZ and CS is the only theory of (co 8  w i)
mixing which is compatible with the fst GWSR. As shown later by Majum
dar [25], Weinberg's first Sum Rule and the vector dominance hypothesis
do not exclude any of the (cogo^) mixing models, i.e., either « mass mixing »
or « current mixing ». What happens is that a particular model of the
(cogo^) mixing demands a particular form of the spectral function sum rule.
For example, in order to have relation (30), it is necessary to assume the
Schwinger term between J* and J { * ] to be zero [25], besides assuming the
1st GWSR and the vector dominance hypothesis.
Relation (29) is more stringent than (27) ; however, it gives no predictions
for 6 Y . In order to predict 6 Y , a precise model for SU 3 symmetrybreaking
is needed. Various models have been presented in the literature:
i) the quark model of Van Royen and Weisskopf [26] ;
ii) two models of the « mass mixing » type by KLZ [16];
iii) three models of the « current mixing » type by KLZ [16], DMO [17],
and OS [18], respectively.
It turns out that the two models of KLZ and OS are in fact identical [27].
We shall just mention one point of the DMO and KLZ + OS models in con
nection with the Generalized Weinberg Sum Rules.
In fact, as pointed out by DasMathurOkubo [17] and by Sakurai [28],
the 2nd GWSR must be abandoned as long as vector meson dominance
approximation is considered valid. This is because, if we assume that the
spectral functions are dominated by the know vector mesons p, co and §,
we have
(31) from the 1st GWSR: g ^ = ^ + ^f ,
y m$ m& m%
(23) from the 2nd GWSR: gg Y = gl r + g Y .
For the consistency of eqs. (31) and (32) it is necessary that m\ = ml> =w,
which does not agree with observation. Das, Mathur and Okubo [17]
and Oakes and Sakurai [18], proposed to change the 2nd GWSR a la Gell
Mann and Okubo, i.e.
The basic SU Z mixing: cog^o^ 315
DMO I dm 2 { Q 3 (m 2 ) + 3&(m 2 ) — 4p 4 (m 2 ) }
r I
2nd GWSR: {e 3 (m 2 ) — &(m 2 )}dm 2 changed into
OsJ^{e 4 (iii a )+3 ft (iii 8 )4 e4 (w a )},
where Q t are the spectral functions and the V s refer to the SU 3 component
in the octet. It is interesting to notice that the DMO proposal [17] clearly
implies that the Weinberg spectral function integral satisfies an octetbreaking
formula, while the OS proposal [18] corresponds to the fact that it is the
inverse propagator matrix for the current that satisfies an octetbreaking
formula (*). These two proposals give different values for B Y . All the above
mentioned theoretical prediction will be reported in Fig. 15, Sect. 5, where
they are compared with experimental data.
4.  The first experimental measurement of the (cogooj.) mixing.
4T. Introduction.  As mentioned in Sect. 1'3, there were two ways of
attempting a direct check of the (cogo^) mixing hypothesis : i) either by using
strong interactions for the production of the vector mesons co and cj>, and
subsequently detecting their rare decay modes into e + e~:
(33)
7r  +p>to+n
'> e + e~,
7i+p^(i>+n
l> e+e~,
or ii) by using the electromagnetic production processes of co and rj> from (e+e~)
collisions, and detecting the o> and <j) via their strong decay modes:
(34)
e + +e~>oo > strong decay modes ,
e + +e _ >(j> > strong decay modes ,
(*) As emphasized by DMO [17], the 2nd GWSR is obtained assuming for the
spectral functions p f 's, superconvergent conditions much stronger than those needed to
obtain the 1st GWSR. This is why one expects the 1st GWSR to be much better than
the 2nd GWSR, and therefore one tries to improve the last one.
316
A. Zichichi
As reported by Ting at the Vienna Conference [29], the first successful
experiment on the direct determination of the (ov^i) mixing angle was done
at CERN by the BolognaCERN Collaboration [30, 31] using reactions (33).
It is obvious from the examination of the final states in reactions (33)
that in order to perform the experiment it is necessary to have a large « neu
tron » detector and a large « electron » detector so as to be able to measure
with good acceptance all particles present in the final states of the above
mentioned reactions.
4*2. The experimental setup.  A schematic diagram of the experimental
setup is shown in Fig. 2. It consists of the following:
i) A system of « beamdefining counters » CUSR : C is a gas Cerenkov
counter to anticoincide the electrons present in the primary beam; U is an
important plastic scintillator counter used in the timing of the neutron;
S is a very thin (0.05 cm) plastic scintillator counter in order to reduce as
much as possible the interactions outside the H 2 target; R is an anticoinci
dence counter to remove beam halo.
ii) A 40 cm long, 5 cm diameter H 2 target. A veto counter, not shown
in Fig. 2, is placed behind the target in order to anticoincide noninteracting
pions.
ShMSng Weill
team Count*™
not to Seal*
Fig. 2.  Showing a schematic diagram of the experimental setup.
iii) Two electron detectors called « top » and « bottom ». In front of
them there are coincidence counters and thinplate spark chambers, which,
for the sake of clarity, have all been omitted in Fig. 2.
iv) Two neutron detectors, called « left » and « right », with anti
coincidente counters G T and G R in front of them to reject charged particles
The basic SU 3 mixing: (Ogi^o^
317
impinging in the « neutron counters ». These two identical neutron detectors
had a sensitive surface and volume equal to 2.16 m 2 and 0.78 w 3 , respectively.
A neutron detector is made of 12 elements of plastic scintillator, each
having dimensions (100 X 18 x 18) cm 3 . Eeach element is viewed by two
XP1040 photomultipliers placed on its two small faces (see Fig. 3). The
NDE
H3^
Fig. 3.  a) Neutron counter assembly, b) The connections between a light guide
and the photomultiplier base are shown.
large volume of scintillator, in the particular geometrical arrangement chosen,
allows a mean detection efficiency of about 26% in the range (40^560)MeV
neutron kinetic energy, for a laboratory solid angle of 0.14 sr at 4 m radial
distance from the centre of the H 2 target. An interesting feature of this
instrument is the accuracy achieved in locating incident particles; this
accuracy is ±1.4 cm for charged particles, and ±2.5 cm for neutrons. The
accuracies achieved for the timeoffiigt measurement are ±0.35 ns for
charged particles and ±0.7 ns for neutrons. It is interesting to note that
the relative timing of all photomultipliers in the neutron counters could be
equalized to ±0.1 ns. An example of this timeequalization is shown in
Fig. 4, where t x is the time difference between the (£/) signal and the signal
from any photomultiplier at one side of the neutron counter, t 2 corresponds
to signals from the other side of the neutron counter, and is the difference
between the two, obtained electronically (*).
(*) For more details on this instrument we refer the reader to Bollini et al. [32].
318 A. Zichichi
nsec
+ 0.1
I
„
•
•
•
•
• —
•
•
•
e

•
— #
•
•
 • • • .
• —
•
•
•
t 2
• • —
•
•
1 1 ■■ .
•
•
1 1
•
JL .
•
• —
— •
•
1 1
•
t,

o.i 
+ 0.1 

0.1 
+ 0.1 

0.1 
1 2 3 A 5 6 7 8 9 10 11 12 Right
Number of the Counter
Fig. 4.  Relative timing of the 12 elements of the neutron detector « Right ».
The abscissa indicates the identification number of an element, the ordinate
the relative timing.
Nr/CH
250
200
150
100
50
POSITION 1.25 10 20 30 40 50 60 70 80 90 98 75 cm
CHANNELS
Fig. 5.  Spatial resolution of a neutron counter, as measured with a muon beam.
Each of the peaks in this spectrum corresponds to a given position of the beam
defining telescope along the neutron counter.
The basic SU Z mixing: cog^cot
319
Typical data on position resolution and linearity of the neutron counters
are shown in Figs. 5 and 6, respectively. In Fig. 5 the curves are labeled with
the distance from the edge of the counter, and the spatial resolution for all
positions in the counter is ±1.4 cm for charged particles. In Fig. 6 the ordi
200 Channels
Fig. 6.  Position calibration of the neutron counters, showing the position of
the muon beam as a function of the channel numbers. The ordinate is also
labeled with the neutron scattering angle, corresponding to 4 m distance for
the counters.
nate is the distance from one edge of the counter, and the abscissa is the
channel number in which the peak corresponding to a certain position (as
shown in Fig. 5) falls. The counter is seen to be linear.
Notice that there is a total of 24 elements. For all of them the above
calibrations were repeated periodically in order to check the correct per
formance of the apparatus. For example, the neutron counter stability over
a week is shown in Fig. la, where the time variation for 6, t x , and t 2 signals
is plotted for each element of the neutron counter. The time stability of the
neutron detector is remarkably good. Figure lb) shows the highvoltage
variation over a period of one week for the « neutronright ».
The neutron detectors measure the timesofflight t n and angles of emission
6 n of neutrons in reactions (33), thus allowing a determination of the missing
masses in reactions (33), i.e., of the mass of the produced meson. The mass
resolution obtained with the above space and time resolutions depends on
the kinematical region in the plane (t n , On) (see Fig. 8). It is ±4 MeV in the
rmass region, ±10 MeV in the comass region, and ±15 MeV in the cj>mass
region.
320
A. Zichichi
o)
So
e 8
d
e
t,
*»
I
<9
v>
m
Ui
»
Z
^4


^
o
m
5^
■
3
Z
1
0.2
0.4 nt«c
02
0.4 rmc
0.2
0.4
b)
VOLT
TYPICAL MAXIMUM VARIATION OF H.V. SUPPLIES OVER A PERIOD OF 1 WEEK
1 VOLT PRODUCES A TIME SHIFT OF 15pMC
RIGHT SIDE 1
RIGHT SIDE 2
PHOTOMULTIPIIERS
Fig. 7.  a) Neutron counter stability over a week: the time variation for 6, t 1 ,
and t 2 signals is plotted for each counter, b) Typical maximum variation of
the highvoltage supplies over a period of one week, for all the photomultipliers
of one neutron detector. Notice that in fact a variation of 1 V produces a 15 ps
shift in the time definition.
The basic SU 3 mixing: cog^o^
321
lT + p— n+V°
p„=2.12GeV/ c
 1 porticUs
(M.V)
20
30
40
60
MO
150
250
0«
100
200
300
400
50°
On
Fig. 8.  The neutron time of flight t n over a 4 m path is plotted vs. the neu
tron emission angle n in the laboratory system. The ordinate on the right refers
to the neutron kinetic energy. The kinematic curves are labeled by the corre
sponding neutron missing masses. The dashed lines indicate constant values
of cos 0* .
The electron detectors are shown in detail in Fig. 9. Each electron detector
consists of nine elements, each one being made of a piece of lead followed
by a twogap spark chamber and a plastic scintillation counter. The first
layer of lead is two radiation lengths thick ; the other layers are one radiation
length thick. The overall detector thickness is half a meter. Before the
first lead layer there are two thinplate spark chambers to allow precise kine
matical reconstruction of the events. Thus a long H 2 target could be used,
when looking for rare events, without losing accuracy in the missingmass
measurement by the neutrons. The two detectors may be rotated independ
ently about a horizontal and vertical axis through the H 2 target.
21
322
A. Zichichi
LEAD
R S
BEAM
H? TARGET
T i ELECTRON DETECTOR
LEAD
LEFT
RIGHT
To neutron detectors
(out of the plane of the page)
ELECTRON DETECTOR
'BOTTOM'
Fig. 9.  Side view of the electron detectors. The M T and M B are scintillation
counters, K T and K B are thinplate spark chambers. Each electron detector
consists of nine layers of lead, spark chamber, and scintillator sandwiched
together.
Figure 10 shows a calibration of one of the two electron detectors. The
response of the telescope is plotted as a function of the energy of the beam.
We see that the instrument is linear. The three sets of points in the upper
curve correspond to measurements made at different times (given by the
run number), and to two different positions of the beam in the detector.
Near the extremes of the detector, the pulseheight decreases and the cali
brations are parametrized according to the maximum depth of the detector
available to the shower. The two lower curves are two of these edgeeffect
calibrations. During the calibrations the detectors were rotated to many
positions, and calibrated as a function of depth and energy in order to allow
the calculation of the total efficiency for any event configuration. For fixed
depths we see that the fluctuations are small; in any case the system was
frequently calibrated in order to be sure that pions were not wrongly identi
fied as electrons.
Figure 11a shows a complete efficiency calibration affixed energy. The
purpose of this figure is to show that the electron detectors « top » and
« bottom » had very similar characteristics. The open circles refer to the
bottom detector and the full circles to the top detector. The electron energy
for these two sets of points in 1050 Me V. Figure 116 shows a family of
curves corresponding to 170 calibration points taken at energies from 1.05 GeV
down to 0.45 GeV.
The basic SU 3 mixing: oigi^Wj
323
Channels
Encoder 10
50
[ (e w ,
«D.
Depth) RUNS
48
*
46

L{Ho.
10 ,
49) 541549
44
%
/
;}(io.
10
49) 582  592
42
\
40
\
\
}[20.
10 .
49) 562570
38
J
j^io.
15 ,
27) 551559
36
34
32
30
28
*
i
i
i
i
\
lit 23,
L 1
16 ,
21) 573580
26
 cot
24
'///'^//'/i'/'
22
20
paoortol
18
16
200 400
600
800 1000 1200 1300
Energy of Electron
Fig. 10.  Calibration of one of the electron detectors. Total scintillation coun
ter pulseheight vs. electron energy.
Table I summarizes the efficiencies of the electron detectors. From as low as
400 MeV up to 1 100 MeV, one can reject pions with a power of ~ 3 x 10~ 4 . For
each particle and each momentum there are three numbers: the electronic
efficiency, the picture analysis efficiency, and their product, the overall
efficiency. As mentioned above, the electron detectors consist of counters
and spark chambers, so there is an electronic rejection in the trigger; then,
once the pictures are taken, there is a further rejection in the picture analysis.
The latter is very important because it allows the elimination of charge exchange
of pions, which is the greatest source of trouble when you want to distinguish
324
A. Zichichi
Fig. 11.  Efficiency calibration of the electron detector as a function of the
depth available to a shower, a) Response of « top » (•) and « bottom » (o)
counters at 1.05 GeV. b) Response of « bottom » counter at different energies.
The curves correspond to 170 calibration points.
a pion from an electron. From 400 MeV to 1100 MeV, the power of the
telescope against pions is practically the same, and the efficiency for electron
detection is very good — between 70 and 80%.
Table I. 
 Efficiency in the e
lectron detector « bottc
im ».
Momentum
(MeV/c)
Par
ticle
Electronic
efficiency (%)
Picture analysis
efficiency (%)
Overall
efficiency (%)
400
1100
e
7T
e
TV
(77.5 ±2.2)
( 6.3±0.2)
(94.0 ±1.5)
(17.6±0.6)
(89.0 ±2.2 )
( 0.43±0.2 )
(88.0 ±2.0 )
( 0.16±0.16)
(69.0±2.6)
( 2.7±1.6)xl0" 4
(83.0±2.3)
( 2.8±2.8)X10~ 4
To summarize, each of the two telescopes has ~ 3 x 10" 4 rejection against
pions, giving a product ~ 10~ 7 , which is the rejection factor for charged nn
pairs and any other sort of charged multipion events. It is this rejection power
that allows the study of rare events such as (e+e") decays of strongly inter
acting particles.
4'3. Some relevant details.  Table II summarizes the most relevant para
meters of the experiment for co and <j> decays into (e+e~). The comass region
and the <j)mass region have been investigated using the same experimental
The basic SU S mixing: cog^co! 325
setup at different angles of acceptance for the neutron and electron detectors,
but changing the primary beam momentum in order to maximize the number
of observable events, i.e. (production crosssection) x (acceptance). For more
details we refer the reader to the original papers (refs. [30] and [31]).
Table II.  Relevant parameters of the to and <j> decay experiments (*).
Parameter
co (ref. [30])
4> (ref. [31])
Pn
1.67 GeV/c
1.93 GeV/c
e i°ab
31°^45°
19°^33°
e c.m.
165°^94°
160°^70°
T a
(42^430) MeV
(95^560) MeV
'«
(46M8) ns
(32^17) ns
a 2
(0.08^0.8) (GeV/c)
i
(0.18M.l) (GeV/c) 2
AM
± 10 MeV
± 15 MeV
G lab
6°^32°
5°425°
o»
32°
36°
T x =
i?! threshold
1.7x(d£/dx) min
2 T
= 28 threshold
150 MeV
22
threshold
700 MeV
(*) p n is the primary pion momentum. It has been chosen at the maximum of the production cross
section. 0^ is the angular range covered by the neutron detectors in the laboratory system. 6° m is the cor
responding value in the centreofmass system. T n is the range of neutron kinetic energies accepted in the
above angular range. It follows the corresponding range of neutron timeofflight / n . q* is the range of four
momentum transfer. AM is the mass uncertainty, dj'^ is the angular range of vectormeson production.
6 D is the angular position of the electron detectors in the vertical plane containing the beam. 7\ and B x are
the thresholds of the first counters in the electron detectors, i.e. after two radiation lengths in lead. S T and
S B are the thresholds of the two electron detectors « top » and « bottom ». These thresholds were fixed at
a very low value of 150 MeV incident electromagnetic energy in order to have high efficiency in the detection
of electromagnetic showers. SS = X T + SB is the total electromagnetic energy released in «top» plus
« bottom ». We trigger every time that the total energy is greater than 700 MeV; again this choice of low
threshold is taken in order to have good detection efficiency for electromagnetic showers originated either by
electrons or photons.
Another important point worth mentioning is the way in which yy events
are rejected. In the description of the electron detectors, it was pointed out
that the rejection power against charged tzk pairs was ~ 10~ 7 . But in (n~p)
interactions, two or more 7i°'s can be produced; 7r°'s decay into y's, which
then materialize in the target or in the plastic scintillator before the thin
plate spark chambers, thus producing electronpositron pairs which can
simulate a genuine e ± from vector meson decay. It is possible to recognize
326
A. Zichichi
most of these yproduced « fake e± », because they are really « electron
positron pairs » whose opening becomes sufficiently large by multiple scatter
ing in the trasversal of the material which is in front of the kinematic spark
chambers. The distribution of the distance between two tracks of a pair is
shown in Fig. 12. The wide part of the spectrum is that expected from
5 10 15 20
OISTANCE BETWEEN TWO TRACKS OF A PAIR IN mm
Fig. 12.  Distribution of the distances in space between the two tracks of an
electronpositron pair.
multiple scattering. The peak at zero is clearly due to a genuine single e±
and not (e+e~) pairs simulating single tracks. In fact, from the measured
distribution (shown in Fig. 12) the number of « fake e± » present in the
The basic SU 3 mixing: cog^Wj
327
peak is expected to be ~ 2. If we now plot the mass distribution of the events
in the peak of Fig. 12, we obtain the distribution shown in Fig. 13.
Notice that this result represents the first successful attempt to resolve
the copeak from the p. As mentioned in the introduction, the experimental
N°ev/30MeV
15~
I ' I ' I i T "  i I ' I " I i I '  r  i  i I i i f  i i i i i
700 800 900 MASS
Fig. 13.  For to > e+e~, mass distribution of e + e~ pairs in the coregion ob
tained with the same type of analysis as in the ^case. The shape of the pdis
tribution is determined by its natural width, the known production distribu
tion and density matrix, and the experimental acceptance and resolution. The
dashed curve is the result of a maximum likelihood fit to the experimental data.
328
A. Zichichi
conditions were chosen in such a way as to minimize the amount of observable
p's. In fact, the broken curve is the expected pmass distribution calculated
from the known production and decay angular distribution combined with
the experimental acceptance.
Repeating the same type of analysis for the <j>case gave the mass distri
bution shown in Fig. 14. In the cf>mass region there is a total of ten events
800 900 1000 noo
MASS (MeV)
Fig. 14.  For <j> > e+e~, the mass distribution for those events with zero opening
distance in Fig. 12.
The basic SU 3 mixing: Wg^co! 329
minus one background events. To have a small background was an essential
feature of the experiment, the limitation in the number of observed <j> > e+e 
being due to the available machine time. Notice the difference between the
distribution shown in Fig. 14 and that of the previous one shown in Fig. 13.
The background below the <j)peak is flat because there is no plike object
in the cj>mass region. In conclusion, a total of nine events of unambiguously
identified § > e + e~ decays were observed.
4*4. Results.  Table III summarize the experimental results obtained on
the (e+e~) decay of co and c> mesons. Let us start with the co column. The first
entry is the direct experimental result obtained. Below there is the copro
duction crosssection which is well known; these two numbers then give the
branching ratio, which together with the total width of the co, taken from the
Rosenfeld tables [33], gives the partial width in the bottom entry.
Table III.  Experimental results of <o and 9 decay.
G)»e+e (ref. [30]) <j>>e+e (ref. [31])
a(np > nV) (67±25) x IO 33 cm 2 (18.4±6.9) x 10 33 cm 2
l> e+e 
o(np > nV) (1.67±0.07) x 10" 27 cm 2 (30±6) x lO" 30 cm 2
Uall
r(V^e+e)/r(V>all) (4.0±1.5)xl0 5 (6.1±2.6)xl0 4
T(V^ all) (*) (12.2±1.3) MeV (3.4±0.8) MeV
r(V^e+e) (0.49±1.19)keV (2.1±0.9) keV
(*) Date taken from the Rosenfeld tables.
In the case of the §, the production crosssection is much lower and it is
not so well known as that of the co. In fact, a point in the ^production
crosssection was measured by the BolognaCERN Collaboration [10],
because when the experiment was started, the 4> production had not been
observed in pionnucleon interactions [34]. The energy at which the (^pro
duction crosssection was measured is slightly higher than that at which the
decay experiment was performed. In fact, a maximum value in the cross
section had still to be found, when a bubble chamber group [35] published
a paper in which the maximum seemed to be 1 50 MeV lower ; so the experi
ment was performed at the lower beam momentum. Notice that the measured
value of the (^production crosssection [10] is in very good agreement with
330 A. Zichichi
the bubble chamber data [35]. Again the total width is taken from the
Rosenfeld tables [33] to derive the partial width.
The value of the generalized mixing angle 6 G was thus determined to be :
tan0 G = , > G = 23°
This result is in excellent agreement with the « current mixing » theory of
Kroll et al. [16] and of Oakes and Sakurai [18] (the slight difference between
the KLZ and OS predictions for 6 G is due to the use of slightly different
mass values, the two models of SU S symmetry breaking being identical [27]).
In connection with previous remarks, the effect of (oop) interference has
also been estimated [36], the result being a variation of ±3° for complete
constructive or destructive interference respectively. It should be noticed,
however, that in the OPE model the (o>p) interference is exactly zero.
Following the theoretical considerations previously reviewed, the results
obtained by the BolognaCERN collaboration led to the following con
clusions [30, 31]:
i) the general idea of (tOgtO]) mixing is confirmed;
ii) the First Generalized Weinberg Spectral Function Sum Rule (satu
rated using only p, to, (j>) is valid within 30 % over all experimental
uncertainty;
iii) there is no evidence for the coupling of the electromagnetic field
to an SU S singlet;
iv) the old A quantum number [37] is not a good quantum number;
v) the fact that (e + e~) decays of co and § are observed with the meas
ured rates is a direct evidence that the J PG quantum numbers of
the co and (j> are indeed 1 .
5.  Present status and conclusions.
The results obtained using strong production reactions (33) were followed
by other measurements of Ting and collaborators at DESY [38] and later
by the Orsay group [39].
Ting studied the photoproduction of p's and of rj>'s, thus obtaining the
partial widths r p ^ e +e and r^ e+e . The DESY result with its uncertainties
for 6q is shown in Fig. 15, where also the Orsay data are plotted. The Orsay
group made use of the (e + e~) storage ring facility in order to determine the
The basic SU Z mixing: cog^c^ 331
partial widths r p ^ +e , /^ e+e , and r^+e. As mentioned previously, the
production reactions are given in eqs. (35)(37),
(35)
(36)
(37)
e+e  ^ p > Tu+Tr 
e+e > to
^7I°Y
./
KK
TC + 7T _ 7l 9
where the vector mesons are produced « electromagnetically » and their
strong decays are observed. The identification of the p, co, (j> is done using
the information coming from the total (e+e~) energy, while the identification
of the final states in the various reactions is performed via the use of geo
metrical constraints on the decay products in the various reactions (35)(37).
All experimental data available so far are reported in Fig. 15, where all
the theoretical predictions are also shown. The diagram is constructed so
as to reproduce in a graphically clear way the fst GWSR, as derived from
DMO [17] and OS [18], i.e., relation (29). Notice that the quark model
prediction [26] numerically satisfies the fst GWSR. This should not be so
strange, as the results of the quark model can be derived from the following
set of assumptions [40] : i) PCAC; ii) First and Second GWSR; iii) pole
dominance in the First and Second GWSR.
It should be emphasized that the two predictions for 6a, ie., that of
DMO [17] and that of KLZ [16] and OS [18], would coincide to first order
SU S symmetrybreaking. These models are all of the « current mixing » type;
they differ only by secondorder SU 3 symmetrybreaking effects. Also the
two « mass mixing » models of KLZ [16] differ only in secondorder SU 3
symmetrybreaking.
It would be misleading to try combining the experimental data of Fig. 15
in the hope of giving an answer to this extremely interesting question which
refers to secondorder SU 3 symmetrybreaking effects. There are, in fact,
no other experiments where secondorder SU 3 symmetrybreaking effects
can so neatly be measured.
332
A. Zichichi
V m <> r (4>— e ++
Fig. 15.  Theoretical predictions and experimental measurements of the (co 8 co x ) mixing.
But we have extended the discussion too far. Let us not forget that a key
point in the great SU 3 castle has withstood the experimental proof: the reason
why the unitarysymmetry mass formula of GellMann and Okubo does
not hold true for the vector meson multiplet is really the (cdgo^) mixing
mechanism. However, the field is now open for checking secondorder
effects in SU 3 symmetrybreaking.
REFERENCES
[1] M. GellMann: Phys. Rev., 125, 1067 (1962); see also Cal. Tech. Report, CTSL20
(1961) (unpublished).
Y. Ne'eman: Nucl. Phys., 26, 222 (1961).
S. Okubo: Progr. Theor. Phys. {Kyoto), 27, 949 (1962).
S. L. Glashow and J. J. Sakurai: Nuovo Cimento, 25, 337 (1962); 26, 622 (1962).
See also M. GellMann: Proc. Intern. Conf. HighEnergy Phys. CERN, p. 533 (1962).
[5] J. J. Sakurai: Phys. Rev. Lett., 9, All (1962).
L. Bertanza, V. Brisson, P. L. Connolly, E. L. Hart, I. S. Mitra, G. C. Moneti,
R. R. Rau, N. P. Samios, I. O. Skillicorn, S. S. Yamamoto, M. Goldberg, L. Gray,
L. Letter, S. Lichtmann and J. Westgard: Phys. Rev. Lett., 9, 180 (1962).
[2]
[3]
[4]
[6]
The basic SU 3 mixing: tOg^o^ 333
[7] J. J. Sakurai: Phys. Rev., 132, 434 (1963).
[8] J. Badier, R. Barloutaud, M. Demoulin, J. Goldberg, B. P. Gregory, D. J. Hol
thuizen, W. Hoogland, J. C. Kluyver, A. Leveque, C. Louedec, J. Meyer, C. Pel
letier, A. Rouge, P. Schlein, A. G. Tenner, A. Verglas, and M. Ville: Phys.
Lett., 17, 337 (1965); G. A. Smith et ah: UCRL 11430 (1964); G. W. London et
ah : BNL 9542 (1965).
[9] S. L. Glashow: Phys. Rev. Lett., 11, 48 (1963).
[10] T. Massam and A. Zichichi: Nuovo Cimento, 44, 309 (1966).
[11] D. Bollini, A. BuhlerBroglin, P. Dalpiaz, T. Massam, F. Navach, F. L. Na
varria, M. A. Schneegans and A. Zichichi: Nuovo Cimento, 60 A, 541 (1969).
[12] P. Dalpiaz, G. Fortunato, T. Massam, Th. Muller and A. Zichichi: An experi
mental proposal to measure the production of (e+e  ) pairs from timelike photons pro
duced in pionnucleon interactions, CERN, 66/197/3/p/jmf.
[13] C. Bernardini, G. F. Corazza, G. Ghigo and B. Touschek: Nuovo Cimento, 18,
1293 (1960).
[14] S. Okubo: Phys. Rev. Lett., 5, 165 (1963).
[15] S. Coleman and H. J. Schnitzer: Phys. Rev., 134 B, 863 (1964).
[16] N. M. Kroll, T. D. Lee and B. Zumino: Phys. Rev., 157, 1376 (1967).
[17] T. Das, V. S. Mathur and S. Okubo: Phys. Rev. Lett., 19, 470 (1967).
[18] R. J. Oakes and J. J. Sakurai: Phys. Rev. Lett., 19, 1266 (1967).
[19] M. GellMann and F. Zachariasen: Phys. Rev., 124, 953 (1961).
[20] G. Feldman and P. I. Mathews: Phys. Rev., 132, 823 (1963).
[21] Y. Nambu and J. J. Sakurai: Phys. Rev. Lett., 8, 79 (1962).
[22] R. Dashen and D. Sharp: Phys. Rev., 133 B, 1585 (1964).
[23] S. Weinberg: Phys. Rev. Lett., 18, 507 (1967). See also T. D. Lee, S. Weinberg and
B. Zumino: Phys. Rev. Lett., 18, 1029 (1967).
[24] K. Kawarabayashi and M. Suzuki: Phys. Rev. Lett., 16, 255 (1966); Riazuddin
and Fayyazuddin: Phys. Rev., 147, 1071 (1966).
[25] D. P. Majumdar: Nuovo Cimento, 57 A, 170 (1968).
[26] R. Van Royen and V. F. Weisskopf: Nuovo Cimento, 50 A, 617 (1967).
[27] N. M. Kroll: Proc. 14th Intern. Conf. HighEnergy Phys., Vienna, 1968, p. 75 (CERN,
Geneva, 1968).
[28] J. J. Sakurai: Phys. Rev. Lett., 19, 803 (1967).
[29] S. C. C. Ting: Proc. Uth Intern. Conf. HighEnergy Phys., Vienna, 1968, p. 43 (CERN,
Geneva, 1968).
[30] D. Bollini, A. BuhlerBroglin, P. Dalpiaz, T. Massam, F. Navach, F. L. Na
varria, M. A. Schneegans and A. Zichichi: Nuovo Cimento, 57 A, 404 (1968).
[31] D. Bollini, A. BuhlerBroglin, P. Dalpiaz, T. Massam, F. Navach, F. L. Na
varria, M. A. Schneegans and A. Zichichi: Nuovo Cimento, 56 A, 1173 (1968).
[32] D. Bollini, A. BuhlerBroglin, P. Dalpiaz, T. Massam, F. Navach, F. L. Na
varria, M. A. Schneegans, F. Zetti and A. Zichichi: Nuovo Cimento, 61 A, 125
(1969).
[33] A. H. Rosenfeld, N. BarashSchmidt, A. BarbaroGaltieri, L. R. Price, P. S6
ding, C. C. Wohl, M. Roos and W. J. Willis: Rev. Mod. Phys., 40, 77 (1968).
[34] L. Bertanza, B. B. Culwick, K. W. Lai, I. S. Mitra, N. P. Samios, A. M. Thorn
dike, S. S. Yamamoto and R. M. Lea: Phys. Rev., 130, 786 (1963); A. Bigi, S. Brandt,
A. De MarcoTrabucco, Ch. Peyrou, R. Sosnowski and A. Wroblewski: Nuovo
Cimento, 33, 1249 (1964); T. P. Wangler, A. R. Erwin and W. D. Walker: Phys.
Rev., 137 B, 414 (1965); D. H. Miller, A. Z. Kovacs, R. McIlwain, T. R. Palfrey
334 A. Zichichi
and G. W. Tautfest: Phys. Rev., 140 B, 360 (1965); J. Bartsch, L. Bondar, R. Speth,
G. Hotop, G. Knies, F. Storim, J M. Brownlee, N. N. Biswar, D. Luers, N. Schmitz,
R. Seeliger and G. P. Wolf: Nuovo Cimento, 43 A, 1010 (1966); O. Goussu, G. Sma
dja and G. Kayas: Nuovo Cimento, 47 A, 383 (1967).
[35] O. A. Dahl, L. M. Hardy, R. I. Hess, J. Kmz and D. H. Miller: Phys. Rev., 163,
1377 (1967); M. A. Abolins, O. I. Dahl, J. S. Danburg, D. Davies, P. Hoch, J. Kirz,
D. H. Miller and R. Rader: Prcc. Intern. Conf. Elementary Particles, Heidelberg
(1967), p. 509 and private communication; G. H. Boyd, A. R. Erven, W. D. Wal
ker and E. West: Phys. Rev., 166, 1458 (1968).
[36] A. Baracca: Nuovo Cimento, 60 A, 633 (1969).
[37] J. B. Bronzan and F. E. Low: Phys. Rev. Lett., 12, 522 (1964).
[38] U. Becker, W. K. Bertram, M. Binkley, C. L. Jordan, T. M. Knasel, R. Mar
shall, D. J. Quinn, M. Rohde, A. J. S. Smith and S. C. C. Ting: Phys. Rev. Lett.,
21, 1504 (1968).
[39] J. E. Augustin, J. C. Bizot, J. Buon, B. Delcourt, J. Haissinski, J. Jeanjean, D. La
lanne, P. C. Marin, H. Nguyen Ngac, J. PerezyJorba, F. Richard, F. Rumpf
and D. Treille: Phys. Lett., 28 B, 508 (1969); 28 B, 513 (1969); 28 B, 517 (1969).
[40] A. Dar and V. F. Weisskopf: Phys. Lett., 26 B, 670 (1968).
List of Papers by Edoardo Amaldi
1) Sulla dispersione anomala del mercurio e del litio (with E. Segre).
Rend. Ace. Lincei, 1, 919921 (1928).
2) Sulla teoria dell'effetto Raman (with E. Segre). Rend. Ace. Lincei, 9,
407409 (1929).
3) Sulla teoria quantistica deU'effetto Raman. Rend. Ace. Lincei, 9, 876
881 (1929).
4) tiber die streuung von Roentgenstrahlen am Wasser. Phys. Z, 32,
914919 (1931).
5) Sulla distribuzione delle molecole in un liquido. Riv. Nuovo Cimento,
9, CXLI (1932).
6) Uber den Ramaneffekt des CO. Z. Phys., 19, 492494 (1932).
7) Ramaneffekt des gasformingen Ammoniaks (with G. Placzek). Nature,
20, 521 (1932)
8) Spettri di assorbimento degli alcalini nel campo elettrico (with E. Segre).
Ric. Scient., 42, 4143 (1933).
9) tiber das Ramanspektrum des gasformigen Ammoniaks (with G.
Placzek). Z. Phys., 81, 259269 (1933).
10) Series of alkaline atoms in an electric field (with E. Segre). Nature,
132, 444 (1933).
11) Effetto del campo elettrico sul limite della serie del potassio (with E.
Segre). Rend. Ace. Lincei, 19, 588594 (1934).
12) Effetto della pressione sui termini elevati degli alcalini (with E. Segre).
Nuovo Cimento, 11, 145156 (1934).
13) Nuovi radioelementi prodotti con bombardamento di neutroni (with
E. Fermi, F. Rasetti, E. Segre). Nuovo Cimento, 11, 442451 (1934).
14) Segno ed energia degli elettroni emessi da elementi attivati con neu
troni (with E. Segre). Nuovo Cimento, 11, 452460 (1934).
15) a) Effetto della pressione sui termini alti della serie degli alcalini (with
E. Segre). Ric. Scient., 5, 53 (1934).
b) Effect of pressure on high terms of alkaline spektra. Nature, 133,
141 (1934).
336 List of papers by Edoardo Amaldi
16) Radioattivita provocata da bombardamento di neutroni. Ill (with
O. D'Agostino. E. Fermi, F. Rasetti, E. Segre). Ric. Scient., 5, 452
453 (1934).
17) Radioattivita provocata da bombardamento di neutroni. IV (with
O. D'Agostino, E. Fermi, F. Rasetti, E. Segre). Ric. Scient., 5 X , 652
653 (1934).
18) Radioattivita provocata da bombardamento di neutroni. V (with
O. D'Agostino, E. Fermi, F. Rasetti, E. Segre). Ric. Scient., 5 2 , 2122
(1934).
19) Azione di sostanze idrogenate sulla radioattivita provocata da neutroni
(with E. Fermi, B. Pontecorvo, F. Rasetti, E. Segre). Ric. Scient., 5 2 ,
282283 (1934).
20) Radioattivita provocata da bombardamento di neutroni. VI (with
O. D'Agostino, E. Segre). Ric. Scient., 5 2 , 381382 (1934).
21) Radioattivita provocata da bombardamento di neutroni. VII (with
O. D'Agostino. E. Fermi, B. Pontecorvo, F. Rasetti, E. Segre). Ric.
Scient., 5 2 , 467470 (1934).
22) Artificial radioactivity produced by neutron bombardament (with E.
Fermi, O. D'Agostino, F. Rasetti. E. Segre). Proc. Royal Soc. {London),
146, 483500 (1934).
23) Le orbite oos degli elementi (with E. Fermi). Mem. Ace. Italia, 6,
119149 (1934).
24) Nuove radioattivita provocate da neutroni. La disintegrazione del boro.
Nuovo Cimento, 12, 223231 (1935).
25) Radioattivita provocata da bombardamento di neutroni. VIII (with
O. D'Agostino, E. Fermi, B. Pontecorvo, F. Rasetti, E. Segre). Ric.
Scient., 6 l5 123125 (1935).
26) Radioattivita indotta da bombardamento di neutroni. IX (with O. D'Ago
stino, E. Fermi, B. Pontecorvo, E. Segre). Ric. Scient., 6 l5 435437
(1935).
27) Radioattivita provocata da bombardamento di neutroni. X (with O.
D'Agostino, E. Fermi, B. Pontecorvo, E. Segre). Ric. Scient., 6 l5 581
584 (1934).
28) Sull'assorbimento dei neutroni lenti (with E. Fermi). Ric. Scient., 6 2 ,
334347 (1935).
29) Sull'assorbimento dei neutroni lenti. II (with E. Fermi). Ric. Scient.,
6 2 , 443447 (1935).
30) Artificial radioactivity produced by neutron bombardament. II (with
O. D'Agostino, E. Fermi, B. Pontecorvo, R. Fasetti, E. Segre). Proc.
Royal Soc. (London), 149 A, 522558 (1935).
31) Einige Spektroskopische Eigenschaften Hochangeregter Atome (with
E. Segre). From the volume in honour of Zeeman, pp. 817 (1935).
List of papers by Edoardo Amaldi 337
32) Sull'assorbimento dei neutroni lenti. Ill (with E. Fermi). Ric. Scient.,
7 lt 5659 (1936).
33) Sul cammino libero medio dei neutroni lenti nella paraffina (with E.
Fermi). Ric. Scient., 7 l9 223225 (1936).
34) Sui gruppi di neutroni lenti (with E. Fermi). Ric. Scient., 7 1? 310313
(1936).
35) Sulle proprieta di diffusione dei neutroni lenti (with E. Fermi). Ric.
Scient., 7 1? 393395 (1936).
36) a) Sopra l'assorbimento e la diffusione di neutroni lenti (with E. Fermi).
Ric. Scient., l x , 454503 (1936).
b) On the absorption and diffusion of slow neutrons (with E. Fermi).
Phys. Rev., 50, 899926 (1936).
37) Behaviour of slow neutrons at different temperatures (with E. Segre).
Phys. Rev., 50, 571 (1936).
38) Un generatore artificiale di neutroni (with E. Fermi, F. Rasetti). Ric.
Scient., 8 2 , 4043 (1937).
39) Kunstliche Radioactivitat durch Neutronen. Phys. Z., 38, 692734 (1937).
40) Neutron yields from artificial sources (with L. R. Hafstad, N. A. Tuve).
Phys. Rev., 51, 896912 (1937).
41) Metodo fotografico per il rilievo della fluttuazione dei raggi X emessi
da un'ampolla (with G. C. Trabacchi). Rend. 1st. Sanita, 1, 317320
(1937).
42) Sulle quantita di sostanze radioattive artificiali che si possono prepa
rare con diversi processi. Atti SIPS (1938).
43) On the albedo of slow neutrons (with E. Fermi, G. C. Wick). Phys.
Rev., 53, 493 (1938).
44) Sopra la conversione interna dei raggi gamma e X del RaD (with F.
Rasetti). Ric. Scient., 10, 111114 (1939).
45) Sulle radiazioni emesse dal gadolinio per cattura dei neutroni lenti
(with F. Rasetti). Ric. Scient., 10, 115118 (1939).
46) Generatore di neutroni a 1.000 kV (with D. Bocciarelli, F. Rasetti,
G. C. Trabacchi). Ric. Scient., 10, 623632 (1939).
47) Sulla diffusione dei neutroni prodotti nella reazione: 12 C+ 2 D = 13 N+ X n
(with D. Bocciarelli, F. Rasetti, G. C. Trabacchi). Ric. Scient., 10,
633637 (1939).
48) On the scattering of neutrons from the C+D reaction (with D. Boc
ciarelli, F. Rasetti, G. C. Trabacchi). Phys. Rev., 56, 881884 (1939).
49) Misura della sezione d'urto elastico fra neutroni e protoni (with D. Boc
ciarelli, G. C. Trabacchi).
a) Atti Ace. d' Italia, 1, 350358 (1940).
b) Ric. Scient., 11, 121127 (1940).
22
338 List of papers by Edoardo Amaldi
50) Sulla scissione degli elementi pesanti (with M. Ageno, D. Bocciarelli,
B. N. Cacciapuoti, G. C. Trabacchi).
a) Atti Ace. <T Italia, 1, 525536 (1940).
b) Ric. Scient., 11, 302311 (1940).
51) Sulla scissione dell'uranio con neutroni veloci (with M. Ageno, D. Boc
ciarelli, G. C. Trabacchi).
a) Atti Ace. <T Italia, 1, 746751 (1940).
b) Ric. Scient., 11, 413417 (1940).
52) Sulla distribuzione angolare dei neutroni emessi nella disintegrazione
di elementi leggeri (with M. Ageno, D. Bocciarelli, G. C. Trabacchi).
Rend. Ace. d* Italia, 2, 338350 (1940).
53) L'impianto generatore di neutroni a 1.000 kilowat dell'Istituto di Sanita
Pubblica (with M. Ageno, D. Bocciarelli, G. C. Trabacchi). Rend. 1st.
Sanita, 3, 201216 (1940).
54) II sistema neutroneprotone. Mem. Ace. d'ltalia, 13, 555615 (1941).
55) Sulla scissione del torio e del protoattinio (with D. Bocciarelli, G. C.
Trabacchi).
a) Ric. Scient., 12, 134138 (1941).
b) Rend. 1st. Sanita, 4, 266272 (1941).
56) Distribuzione angolare di raggi y emessi nella reazione: 1 H+ 7 Li =
= 8 Be+y (with M. Ageno, D. Bocciarelli, G. C. Trabacchi).
a) Ric. Scient., 12, 139143 (1941).
b) Rend. 1st. Sanita, 4, 260265 (1941).
57) Sull'urto fra protoni e neutroni. I (with M. Ageno, D. Bocciarelli,
G. C. Trabacchi). Ric. Scient., 12, 830842 (1941).
58) Fission yield by fast neutrons (with M. Ageno, D. Bocciarelli, B. N.
Cacciapuoti, G. C. Trabacchi). Phys. Rev., 60, 6775 (1941).
59) Sull'urto fra protoni e neutroni. II (with D. Bocciarelli, B. Ferretti,
G. C. Trabacchi). Ric. Scient., 13, 502531 (1942).
60) Tubo a raggi X con catodo sostituibile (with D. Bocciarelli, G. C. Tra
bacchi). Rend. 1st. Sanita, 5, 694698 (1942).
61) Streuung von 14MVNeutronen an Protonen (with D. Bocciarelli,
B. Ferretti, G. C. Trabacchi). Naturwiss., 30, 582583 (1942).
62) Sull'urto di neutroni contro protoni e deutoni (with M. Ageno, D. Boc
ciarelli, G. C. Trabacchi).
a) Nuovo Cimento, 1, 253278 (1943).
b) Gazz. Chim. Ital, 75 (1943).
63) Apparecchio per la purificazione e la conservazione di idrogeno desti
nato a produzione di ioni (with D. Bocciarelli, G. C. Trabacchi).
a) Rend. 1st. Sanita, 6, 416419 (1943).
b) Gazz. di Chim., 74, 127130 (1944).
64) Streuung von schnellen Neutronen an Protonen und Deuteronen (with
M. Ageno, D. Bocciarelli, B. N. Cacciapuoti, G. C. Trabacchi). Natur
wiss., 31, 231232 (1943).
List of papers by Edoardo Amaldi 339
65) Effetti di diffrazione nello sparpagliamento dei neutroni veloci (with
D. Bocciarelli, B. N. Cacciapuoti, G. C. Trabacchi).
a) Atti Ace. Lincei, 1, 2934 (1946).
b) Rend. 1st. Sanitd, 9, 513 (1946).
66) Contribute* alia teoria dell'acceleratore a induzione (with B. Ferretti).
Atti Ace. Lincei, 1, 8589 (1946).
67) Sue due varianti dell'acceleratore a induzione (with B. Ferretti). Nuovo
Cimento, 3, 2239 (1946).
68) Sullo sparpagliamento elastico dei neutroni veloci da parte di nuclei
medi e pesanti (with D. Bocciarelli, B. N. Cacciapuoti, G. C. Trabacchi).
a) Nuovo Cimento, 3, 203234 (1946).
b) Rend. 1st. Sanitd, 9, 687724 (1946).
69) On two possible modifications of the induction accelerator (with B.
Ferretti). Rev. Scient. Instr., 17, 389395 (1946).
70) On the scattering of fast neutrons by protons and deuterons (with
M. Ageno, D. Bocciarelli, G. C. Trabacchi). Phys. Rev., 71, 3031 (1947).
71) a) Sulla dipendenza del raggio nucleare dal peso atomico (with B. N.
Cacciapuoti). Atti Ace. Lincei. 2, 243246 (1947).
b) On the dependence of nuclear radius on the mass number (with
B. N. Cacciapuoti). Phys. Rev., 71, 739740 (1947).
72) The elastic scattering of fast neutrons by medium and heavy nuclei
(with D. Bocciarelli, B. N. Cacciapuoti, G. C. Trabacchi). Phys. Soc.
Cambr. Conf. Report, 97113 (1947).
73) A research for anomalous scattering of [xmesons by nucleons (with
G. Fidecaro). Helv. Phys. Acta, 23, 93102 (1950).
74) Contributo alio studio degli sciami estesi. I (with C. Castagnoli, A. Gigli,
S. Sciuti). Nuovo Cimento, 7, 401456 (1950).
75) An experiment on the anomalous scattering of fast [xmesons by nucleons
(with G. Fidecaro). Nuovo Cimento, 7, 535552 (1950).
76) On the Coulomb scattering of (xmesons by light nuclei (with G. Fide
caro, F. Mariani). Nuovo Cimento, 7, 553574 (1950).
77) Sull'effetto di transizione nel fenomeno di produzione di stelle da parte
della radiazione cosmica (with C. Castagnoli, A. Gigli, S. Sciuti). Nuovo
Cimento, 7, 697699 (1950).
78) On the influence of the spin interaction on the scattering of mesons
and electrons by licht nuclei (with G. Fidecaro, F. Mariani). Nuovo
Cimento, 7, 757773 (1950).
79) Contributo alio studio degli sciami estesi. II (with C. Castagnoli, A.
Gigli, S. Sciuti). Nuovo Cimento, 7, 816834 (1950).
80) An experiment on the anomalous scattering of ^mesons by nucleons
(with G. Fidecaro). Phys. Rev., 81, 338341 (1951).
340 List of papers by Edoardo Amaldi
81) Diffraction effects in the scattering of neutrons, mesons, and electrons
by nuclei. Ripon Professorship Lecture, 1951, delivered in the Indian
Associations for the Cultivation of Science, Jadapur, Calcutta 32, in
January 1951.
82) On the interaction of cosmic rays with matter under 50 metres water
equivalent (with C. Castagnoli, A. Gigli, S. Sciuti). Nuovo Cimento, 9,
453455 (1952).
83) An anticoincidence experiment on cosmic rays at a depth of 50 metres
water equivalent (with C. Castagnoli, S. Sciuti, A. Gigli). Proc. Phys.
Soc., A 65, 556558 (1952).
84) On the interaction of cosmic rays with matter under 50 metres water
equivalent. II (with C. Castagnoli, A. Gigli, S. Sciuti). Nuovo Cimento,
9, 9691003 (1952).
85) On the longitudinal development of air showers according to Fermi's
theory of meson production (with L. Mezzetti, G. Stoppini). Nuovo
Cimento, 10, 803816 (1953).
86) Underground experiments in Europe. Proc. Intern. Conf. Theoretical
Physics (KyotoTokyo), September 1953.
87) Contribution to the taumeson investigation (with G. Baroni, C. Casta
gnoli, G. Cortini, A. Manfredini). Nuovo Cimento, 10, 937948 (1953).
88) Preliminary research on V\ events in emulsion (with C. Castagnoli,
G. Cortini, A. Manfredini). Nuovo Cimento, 10, 13511353 (1953).
89) On a possible negative K > rcmeson decay (with G. Baroni, C. Casta
gnoli, G. Cortini, C. Franzinetti, A. Manfredini). Nuovo Cimento, 11,
207209 (1954).
90) Lifetimes measurement of unstable charged particles of cosmic radia
tion using emulsion (with C. Castagnoli, G. Cortini, C. Franzinetti).
Nuovo Cimento, 12, 668676 (1954).
91) On the interaction of fast fxmesons with matter. Suppl. al Nuovo Cimento,
11, 406413 (1954).
92) Contribution to the jjimeson investigation (with G. Baroni, G. Cortini,
C. Franzinetti). Suppl. al Nuovo Cimento, 12, 181184 (1954).
93) Contribution to the Kmeson investigation (with G. Cortini, A. Man
fredini). Suppl. al Nuovo Cimento, 12, 205206 (1954).
94) On the longitudinal development of air showers according to Fermi's
Theory of meson production (with G. Stoppini). Memorie del V Con
gresso Inter nazionale de Radiation Cosmica, Mexico 1958.
95) Unusual event produced by cosmic ray (with C. Castagnoli, G. Cortini,
C. Franzinetti, A. Manfredini). Nuovo Cimento, 1, 492500 (1955).
96) On the measurement of the mean lifetime of strange particles. Suppl.
al Nuovo Cimento, 2, 253 (1955).
List of papers by Edoardo Amaldi 341
97) a) Su di una Stella provocata da un antiprotone osservato in emul
sioni nucleari (with. O. Chamberlain, W. Chupp, G. Goldhaber, E.
Segre, C. Wiegand, G. Baroni, C. Castagnoli, C. Franzinetti, A. Man
fredini). Rend. Ace. Lincei, Ser. VIII, 19, 381 (1955).
b) Antiproton star observed in emulsion (with O. Chamberlain, W.
Chupp, G. Goldhaber, E. Segre, C. Wiegand, G. Baroni, C. Castagnoli,
C. Franzinetti, A. Manfredini). Phys. Rev., 101, 909 (1956).
98) On the observation of an antiproton star in emulsion exposed at the
Bevatron (with O. Chamberlain, W. Chupp, G. Goldhaber, E. Segre,
C. Wiegand, G. Baroni, C. Castagnoli). Nuovo Cimento, 3, 447 (1956).
99) Example of an antinucleon annihilation (with O. Chamberlain, W.
Chupp, A. G. Ekspong, G. Goldhaber, S. Goldhaber, E. J. Lofgren,
C. Wiegand, G. Baroni, C. Castagnoli, C. Franzinetti, A. Manfredini).
Phys. Rev., 102, 921 (1956).
100) An electronic scanner for nuclear emulsion (with C. Castagnoli C.
Franzinetti). Nuovo Cimento, 4, 11651173 (1956).
101) Report on the Tmesons. Nuovo Cimento Suppl. al Vol. 4, n. 2 179215
(1956).
102) Antiprotonnucleon annihilation process (antiproton collaboration
experiment) (with W. H. Barkas, R. W. Birge, W. W. Chupp, A.
G. Ekspong, G. Goldhaber, S. Goldhaber, H. H. Heckman, D. H.
Perkins, J. Sanweiss, E. Segre, F. M. Smith, D. H. Stork, L. van
Rossum). Phys. Rev., 105, 3, 10371058 (1957).
103) Further results on antiproton annihilations (with C. Castagnoli, M.
FerroLuzzi, C. Franzinetti, A. Manfredini). Nuovo Cimento, 5, 1797
1800 (1957).
104) The production and slowing down of neutrons. Handbuck der Physik,
Vol. XXXVIII/2 pp. 1659 (Springer Verlag, Berlin, 1959).
105) Study of antiproton with emulsion technique (with G. Baroni, G.
Bellettini, C. Castagnoli, M. FerroLuzzi, A. Manfredini). Nuovo
Cimento, 14, 9771026 (1959).
106) Production and decay of an antisigma+ (with A. BarbaroGaltieri,
G. Baroni, C. Castagnoli, M. FerroLuzzi, A. Manfredini, M, Muchinik,
V. Rossi e M. Severi). Nuovo Cimento, 16, 392395 (1960).
107) Le antiparticelle. Suppl. al Nuovo Cimento, 19, 101 (1961).
108) Search for Dirac magnetic poles (with G. Baroni, H. Bradner, H. G. de
Carvalho, L. Hoffmann, A. Manfredini e G. Vanderhaeghe). Comptes
Rendus de la Conf. Intern. d'AixenProvence, sur le Particules elemen
taires, 155(1961).
109) Experimental data on spectral variations during forbush (with F. Ba
chelet, P. Balata, N. Iucci). Pontificiae Academiae Scientiarum Scripta
Varia. Semaine d'Etude dur le probleme du Rayonnement cosmique
dans l'espace interplanetaire 16 October 1962, p. 299.
342 List of papers by Edoardo Amaldi
110) Search for Dirac magnetic poles (with G. Baroni, A. Manfredini, H.
Bradner, L. Hoffmann, G. Vanderaeghe). Nuovo Cimento, 28, 773 (1963).
111) Search for Dirac magnetic poles (wi h G. Baroni, H. Bradner, H. G. de
Carvalho, L. Hoffmann, A. Manfredini e G. Vanderaeghe). CERN 6313
Nuclear Physics Division, 10th April 1963.
1 12) Polarization of recoil protons in ep elastic scattering (with E. Gans
sauge, R. Gomez, G. Gorini, S. Penner, S. Serbassi, G. Stoppini, M.
L. Vincelli). Nuovo Cimento, 39, 474 (9165).
113) Experimental search for a possible change of the beta decay constant
with centrifugae forces (with M. Ageno). Atti Ace. Lincei, Memorie, 8,
Sez. II, fase I (1966).
114) Realta naturale e teorie scientifiche, in Saggi su Galileo, 1967.
115) On the Dirac magnetic poles, in Old and new Problems in Elementary
Particles edited by G. Puppi (Academic Press, New York, 1968).
116) Ricordo di Ettore Majorana. Giornale di Fisica, 9, n. 4 (1968).
117) L' opera scientifica di Ettore Majorana. Phyxics, 9, 3 (1968). See also
La vita e V opera di Ettore Majorana (19061938). Accademia Nazionale
dei Lincei (1966).
118) A measurement of pion electroproduction crosssection near threshold
(with M. Balla, B. Borgia, G. V. Di Giorgio, A. Giazotto, M. Giorgi,
P. Pistilli, S. Serbassi, G. Stoppini). Lett. Nuovo Cimento, 1, 247 (1969).
Not included in the list, a number of books of physics for high school, written in co
operation with Ginestra Amaldi.
Tipografia Compositori  Bologna  Italy